LMFDB - Embedded newform 5054.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.53209 q^{3} +1.00000 q^{4} -0.652704 q^{5} -2.53209 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.41147 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.53209 q^{3} +1.00000 q^{4} -0.652704 q^{5} -2.53209 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.41147 q^{9} -0.652704 q^{10} +0.532089 q^{11} -2.53209 q^{12} +1.87939 q^{13} +1.00000 q^{14} +1.65270 q^{15} +1.00000 q^{16} -1.04189 q^{17} +3.41147 q^{18} -0.652704 q^{20} -2.53209 q^{21} +0.532089 q^{22} -8.82295 q^{23} -2.53209 q^{24} -4.57398 q^{25} +1.87939 q^{26} -1.04189 q^{27} +1.00000 q^{28} -4.81521 q^{29} +1.65270 q^{30} +5.59627 q^{31} +1.00000 q^{32} -1.34730 q^{33} -1.04189 q^{34} -0.652704 q^{35} +3.41147 q^{36} +6.90167 q^{37} -4.75877 q^{39} -0.652704 q^{40} +2.79561 q^{41} -2.53209 q^{42} -7.36959 q^{43} +0.532089 q^{44} -2.22668 q^{45} -8.82295 q^{46} -0.411474 q^{47} -2.53209 q^{48} +1.00000 q^{49} -4.57398 q^{50} +2.63816 q^{51} +1.87939 q^{52} +1.98545 q^{53} -1.04189 q^{54} -0.347296 q^{55} +1.00000 q^{56} -4.81521 q^{58} +2.73648 q^{59} +1.65270 q^{60} -6.69459 q^{61} +5.59627 q^{62} +3.41147 q^{63} +1.00000 q^{64} -1.22668 q^{65} -1.34730 q^{66} +3.43107 q^{67} -1.04189 q^{68} +22.3405 q^{69} -0.652704 q^{70} -0.554378 q^{71} +3.41147 q^{72} +0.170245 q^{73} +6.90167 q^{74} +11.5817 q^{75} +0.532089 q^{77} -4.75877 q^{78} -11.3969 q^{79} -0.652704 q^{80} -7.59627 q^{81} +2.79561 q^{82} +10.6382 q^{83} -2.53209 q^{84} +0.680045 q^{85} -7.36959 q^{86} +12.1925 q^{87} +0.532089 q^{88} +12.4047 q^{89} -2.22668 q^{90} +1.87939 q^{91} -8.82295 q^{92} -14.1702 q^{93} -0.411474 q^{94} -2.53209 q^{96} +5.38919 q^{97} +1.00000 q^{98} +1.81521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 3 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} - 6 q^{46} + 9 q^{47} - 3 q^{48} + 3 q^{49} - 6 q^{50} - 9 q^{51} - 12 q^{53} + 3 q^{56} - 18 q^{58} + 3 q^{59} + 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} + 3 q^{65} - 3 q^{66} + 3 q^{67} + 24 q^{69} - 3 q^{70} + 9 q^{71} - 21 q^{73} + 9 q^{74} + 3 q^{75} - 3 q^{77} - 3 q^{78} - 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} - 3 q^{84} - 18 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} - 15 q^{89} - 6 q^{92} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 3 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 - 6 * q^46 + 9 * q^47 - 3 * q^48 + 3 * q^49 - 6 * q^50 - 9 * q^51 - 12 * q^53 + 3 * q^56 - 18 * q^58 + 3 * q^59 + 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 + 3 * q^65 - 3 * q^66 + 3 * q^67 + 24 * q^69 - 3 * q^70 + 9 * q^71 - 21 * q^73 + 9 * q^74 + 3 * q^75 - 3 * q^77 - 3 * q^78 - 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 - 3 * q^84 - 18 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 - 15 * q^89 - 6 * q^92 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 3 * q^98 + 9 * 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
$3$	−2.53209	−1.46190	−0.730951	−	0.682430i	$-0.760923\pi$
$3$	−2.53209	−1.46190	−0.730951	+	0.682430i	$0.760923\pi$
$4$	1.00000	0.500000
$5$	−0.652704	−0.291898	−0.145949	−	0.989292i	$-0.546624\pi$
$5$	−0.652704	−0.291898	−0.145949	+	0.989292i	$0.546624\pi$
$6$	−2.53209	−1.03372
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.41147	1.13716
$10$	−0.652704	−0.206403
$11$	0.532089	0.160431	0.0802154	−	0.996778i	$-0.474439\pi$
$11$	0.532089	0.160431	0.0802154	+	0.996778i	$0.474439\pi$
$12$	−2.53209	−0.730951
$13$	1.87939	0.521248	0.260624	−	0.965440i	$-0.416072\pi$
$13$	1.87939	0.521248	0.260624	+	0.965440i	$0.416072\pi$
$14$	1.00000	0.267261
$15$	1.65270	0.426726
$16$	1.00000	0.250000
$17$	−1.04189	−0.252695	−0.126348	−	0.991986i	$-0.540325\pi$
$17$	−1.04189	−0.252695	−0.126348	+	0.991986i	$0.540325\pi$
$18$	3.41147	0.804092
$19$	0	0
$19$	0	0
$20$	−0.652704	−0.145949
$21$	−2.53209	−0.552547
$22$	0.532089	0.113442
$23$	−8.82295	−1.83971	−0.919856	−	0.392256i	$-0.871695\pi$
$23$	−8.82295	−1.83971	−0.919856	+	0.392256i	$0.871695\pi$
$24$	−2.53209	−0.516860
$25$	−4.57398	−0.914796
$26$	1.87939	0.368578
$27$	−1.04189	−0.200512
$28$	1.00000	0.188982
$29$	−4.81521	−0.894162	−0.447081	−	0.894494i	$-0.647536\pi$
$29$	−4.81521	−0.894162	−0.447081	+	0.894494i	$0.647536\pi$
$30$	1.65270	0.301741
$31$	5.59627	1.00512	0.502560	−	0.864543i	$-0.332392\pi$
$31$	5.59627	1.00512	0.502560	+	0.864543i	$0.332392\pi$
$32$	1.00000	0.176777
$33$	−1.34730	−0.234534
$34$	−1.04189	−0.178683
$35$	−0.652704	−0.110327
$36$	3.41147	0.568579
$37$	6.90167	1.13463	0.567314	−	0.823501i	$-0.307983\pi$
$37$	6.90167	1.13463	0.567314	+	0.823501i	$0.307983\pi$
$38$	0	0
$39$	−4.75877	−0.762013
$40$	−0.652704	−0.103202
$41$	2.79561	0.436600	0.218300	−	0.975882i	$-0.429949\pi$
$41$	2.79561	0.436600	0.218300	+	0.975882i	$0.429949\pi$
$42$	−2.53209	−0.390710
$43$	−7.36959	−1.12385	−0.561926	−	0.827188i	$-0.689939\pi$
$43$	−7.36959	−1.12385	−0.561926	+	0.827188i	$0.689939\pi$
$44$	0.532089	0.0802154
$45$	−2.22668	−0.331934
$46$	−8.82295	−1.30087
$47$	−0.411474	−0.0600197	−0.0300098	−	0.999550i	$-0.509554\pi$
$47$	−0.411474	−0.0600197	−0.0300098	+	0.999550i	$0.509554\pi$
$48$	−2.53209	−0.365476
$49$	1.00000	0.142857
$50$	−4.57398	−0.646858
$51$	2.63816	0.369416
$52$	1.87939	0.260624
$53$	1.98545	0.272723	0.136361	−	0.990659i	$-0.456459\pi$
$53$	1.98545	0.272723	0.136361	+	0.990659i	$0.456459\pi$
$54$	−1.04189	−0.141783
$55$	−0.347296	−0.0468294
$56$	1.00000	0.133631
$57$	0	0
$58$	−4.81521	−0.632268
$59$	2.73648	0.356260	0.178130	−	0.984007i	$-0.442995\pi$
$59$	2.73648	0.356260	0.178130	+	0.984007i	$0.442995\pi$
$60$	1.65270	0.213363
$61$	−6.69459	−0.857155	−0.428577	−	0.903505i	$-0.640985\pi$
$61$	−6.69459	−0.857155	−0.428577	+	0.903505i	$0.640985\pi$
$62$	5.59627	0.710727
$63$	3.41147	0.429805
$64$	1.00000	0.125000
$65$	−1.22668	−0.152151
$66$	−1.34730	−0.165841
$67$	3.43107	0.419172	0.209586	−	0.977790i	$-0.432788\pi$
$67$	3.43107	0.419172	0.209586	+	0.977790i	$0.432788\pi$
$68$	−1.04189	−0.126348
$69$	22.3405	2.68948
$70$	−0.652704	−0.0780130
$71$	−0.554378	−0.0657925	−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378	−0.0657925	−0.0328963	+	0.999459i	$0.510473\pi$
$72$	3.41147	0.402046
$73$	0.170245	0.0199256	0.00996281	−	0.999950i	$-0.496829\pi$
$73$	0.170245	0.0199256	0.00996281	+	0.999950i	$0.496829\pi$
$74$	6.90167	0.802303
$75$	11.5817	1.33734
$76$	0	0
$77$	0.532089	0.0606372
$78$	−4.75877	−0.538825
$79$	−11.3969	−1.28225	−0.641127	−	0.767435i	$-0.721533\pi$
$79$	−11.3969	−1.28225	−0.641127	+	0.767435i	$0.721533\pi$
$80$	−0.652704	−0.0729745
$81$	−7.59627	−0.844030
$82$	2.79561	0.308723
$83$	10.6382	1.16769	0.583845	−	0.811865i	$-0.301548\pi$
$83$	10.6382	1.16769	0.583845	+	0.811865i	$0.301548\pi$
$84$	−2.53209	−0.276274
$85$	0.680045	0.0737612
$86$	−7.36959	−0.794683
$87$	12.1925	1.30718
$88$	0.532089	0.0567209
$89$	12.4047	1.31489	0.657446	−	0.753502i	$-0.271637\pi$
$89$	12.4047	1.31489	0.657446	+	0.753502i	$0.271637\pi$
$90$	−2.22668	−0.234713
$91$	1.87939	0.197013
$92$	−8.82295	−0.919856
$93$	−14.1702	−1.46939
$94$	−0.411474	−0.0424403
$95$	0	0
$96$	−2.53209	−0.258430
$97$	5.38919	0.547189	0.273594	−	0.961845i	$-0.411787\pi$
$97$	5.38919	0.547189	0.273594	+	0.961845i	$0.411787\pi$
$98$	1.00000	0.101015
$99$	1.81521	0.182435
$100$	−4.57398	−0.457398
$101$	−4.43376	−0.441176	−0.220588	−	0.975367i	$-0.570798\pi$
$101$	−4.43376	−0.441176	−0.220588	+	0.975367i	$0.570798\pi$
$102$	2.63816	0.261216
$103$	−18.5672	−1.82948	−0.914739	−	0.404046i	$-0.867604\pi$
$103$	−18.5672	−1.82948	−0.914739	+	0.404046i	$0.867604\pi$
$104$	1.87939	0.184289
$105$	1.65270	0.161287
$106$	1.98545	0.192844
$107$	0.248970	0.0240689	0.0120344	−	0.999928i	$-0.496169\pi$
$107$	0.248970	0.0240689	0.0120344	+	0.999928i	$0.496169\pi$
$108$	−1.04189	−0.100256
$109$	−18.7743	−1.79825	−0.899124	−	0.437695i	$-0.855795\pi$
$109$	−18.7743	−1.79825	−0.899124	+	0.437695i	$0.855795\pi$
$110$	−0.347296	−0.0331134
$111$	−17.4757	−1.65872
$112$	1.00000	0.0944911
$113$	5.45336	0.513009	0.256505	−	0.966543i	$-0.417429\pi$
$113$	5.45336	0.513009	0.256505	+	0.966543i	$0.417429\pi$
$114$	0	0
$115$	5.75877	0.537008
$116$	−4.81521	−0.447081
$117$	6.41147	0.592741
$118$	2.73648	0.251914
$119$	−1.04189	−0.0955098
$120$	1.65270	0.150871
$121$	−10.7169	−0.974262
$122$	−6.69459	−0.606100
$123$	−7.07873	−0.638267
$124$	5.59627	0.502560
$125$	6.24897	0.558925
$126$	3.41147	0.303918
$127$	−9.72193	−0.862682	−0.431341	−	0.902189i	$-0.641959\pi$
$127$	−9.72193	−0.862682	−0.431341	+	0.902189i	$0.641959\pi$
$128$	1.00000	0.0883883
$129$	18.6604	1.64296
$130$	−1.22668	−0.107587
$131$	10.5398	0.920869	0.460435	−	0.887694i	$-0.347694\pi$
$131$	10.5398	0.920869	0.460435	+	0.887694i	$0.347694\pi$
$132$	−1.34730	−0.117267
$133$	0	0
$134$	3.43107	0.296400
$135$	0.680045	0.0585289
$136$	−1.04189	−0.0893413
$137$	18.4611	1.57724	0.788619	−	0.614882i	$-0.210796\pi$
$137$	18.4611	1.57724	0.788619	+	0.614882i	$0.210796\pi$
$138$	22.3405	1.90175
$139$	−21.3182	−1.80819	−0.904093	−	0.427336i	$-0.859452\pi$
$139$	−21.3182	−1.80819	−0.904093	+	0.427336i	$0.859452\pi$
$140$	−0.652704	−0.0551635
$141$	1.04189	0.0877429
$142$	−0.554378	−0.0465223
$143$	1.00000	0.0836242
$144$	3.41147	0.284290
$145$	3.14290	0.261004
$146$	0.170245	0.0140895
$147$	−2.53209	−0.208843
$148$	6.90167	0.567314
$149$	9.86484	0.808159	0.404079	−	0.914724i	$-0.367592\pi$
$149$	9.86484	0.808159	0.404079	+	0.914724i	$0.367592\pi$
$150$	11.5817	0.945643
$151$	2.86484	0.233137	0.116569	−	0.993183i	$-0.462811\pi$
$151$	2.86484	0.233137	0.116569	+	0.993183i	$0.462811\pi$
$152$	0	0
$153$	−3.55438	−0.287354
$154$	0.532089	0.0428769
$155$	−3.65270	−0.293392
$156$	−4.75877	−0.381007
$157$	2.39693	0.191296	0.0956478	−	0.995415i	$-0.469508\pi$
$157$	2.39693	0.191296	0.0956478	+	0.995415i	$0.469508\pi$
$158$	−11.3969	−0.906691
$159$	−5.02734	−0.398694
$160$	−0.652704	−0.0516008
$161$	−8.82295	−0.695346
$162$	−7.59627	−0.596819
$163$	−19.8794	−1.55707	−0.778537	−	0.627599i	$-0.784038\pi$
$163$	−19.8794	−1.55707	−0.778537	+	0.627599i	$0.784038\pi$
$164$	2.79561	0.218300
$165$	0.879385	0.0684600
$166$	10.6382	0.825681
$167$	9.92127	0.767731	0.383866	−	0.923389i	$-0.374593\pi$
$167$	9.92127	0.767731	0.383866	+	0.923389i	$0.374593\pi$
$168$	−2.53209	−0.195355
$169$	−9.46791	−0.728301
$170$	0.680045	0.0521571
$171$	0	0
$172$	−7.36959	−0.561926
$173$	−24.9864	−1.89968	−0.949840	−	0.312737i	$-0.898754\pi$
$173$	−24.9864	−1.89968	−0.949840	+	0.312737i	$0.898754\pi$
$174$	12.1925	0.924314
$175$	−4.57398	−0.345760
$176$	0.532089	0.0401077
$177$	−6.92902	−0.520817
$178$	12.4047	0.929769
$179$	−21.6168	−1.61572	−0.807858	−	0.589377i	$-0.799373\pi$
$179$	−21.6168	−1.61572	−0.807858	+	0.589377i	$0.799373\pi$
$180$	−2.22668	−0.165967
$181$	−0.475652	−0.0353549	−0.0176775	−	0.999844i	$-0.505627\pi$
$181$	−0.475652	−0.0353549	−0.0176775	+	0.999844i	$0.505627\pi$
$182$	1.87939	0.139309
$183$	16.9513	1.25308
$184$	−8.82295	−0.650436
$185$	−4.50475	−0.331196
$186$	−14.1702	−1.03901
$187$	−0.554378	−0.0405401
$188$	−0.411474	−0.0300098
$189$	−1.04189	−0.0757863
$190$	0	0
$191$	−13.4115	−0.970420	−0.485210	−	0.874398i	$-0.661257\pi$
$191$	−13.4115	−0.970420	−0.485210	+	0.874398i	$0.661257\pi$
$192$	−2.53209	−0.182738
$193$	−10.5466	−0.759164	−0.379582	−	0.925158i	$-0.623932\pi$
$193$	−10.5466	−0.759164	−0.379582	+	0.925158i	$0.623932\pi$
$194$	5.38919	0.386921
$195$	3.10607	0.222430
$196$	1.00000	0.0714286
$197$	−10.4483	−0.744411	−0.372206	−	0.928150i	$-0.621398\pi$
$197$	−10.4483	−0.744411	−0.372206	+	0.928150i	$0.621398\pi$
$198$	1.81521	0.129001
$199$	−12.9804	−0.920156	−0.460078	−	0.887878i	$-0.652179\pi$
$199$	−12.9804	−0.920156	−0.460078	+	0.887878i	$0.652179\pi$
$200$	−4.57398	−0.323429
$201$	−8.68779	−0.612789
$202$	−4.43376	−0.311958
$203$	−4.81521	−0.337961
$204$	2.63816	0.184708
$205$	−1.82470	−0.127443
$206$	−18.5672	−1.29364
$207$	−30.0993	−2.09204
$208$	1.87939	0.130312
$209$	0	0
$210$	1.65270	0.114047
$211$	12.0273	0.827996	0.413998	−	0.910278i	$-0.364132\pi$
$211$	12.0273	0.827996	0.413998	+	0.910278i	$0.364132\pi$
$212$	1.98545	0.136361
$213$	1.40373	0.0961822
$214$	0.248970	0.0170193
$215$	4.81016	0.328050
$216$	−1.04189	−0.0708916
$217$	5.59627	0.379899
$218$	−18.7743	−1.27155
$219$	−0.431074	−0.0291293
$220$	−0.347296	−0.0234147
$221$	−1.95811	−0.131717
$222$	−17.4757	−1.17289
$223$	−16.1634	−1.08238	−0.541192	−	0.840899i	$-0.682027\pi$
$223$	−16.1634	−1.08238	−0.541192	+	0.840899i	$0.682027\pi$
$224$	1.00000	0.0668153
$225$	−15.6040	−1.04027
$226$	5.45336	0.362752
$227$	−10.8844	−0.722426	−0.361213	−	0.932483i	$-0.617637\pi$
$227$	−10.8844	−0.722426	−0.361213	+	0.932483i	$0.617637\pi$
$228$	0	0
$229$	−13.3841	−0.884448	−0.442224	−	0.896905i	$-0.645810\pi$
$229$	−13.3841	−0.884448	−0.442224	+	0.896905i	$0.645810\pi$
$230$	5.75877	0.379722
$231$	−1.34730	−0.0886456
$232$	−4.81521	−0.316134
$233$	19.6432	1.28687	0.643435	−	0.765501i	$-0.277509\pi$
$233$	19.6432	1.28687	0.643435	+	0.765501i	$0.277509\pi$
$234$	6.41147	0.419131
$235$	0.268571	0.0175196
$236$	2.73648	0.178130
$237$	28.8580	1.87453
$238$	−1.04189	−0.0675356
$239$	−20.4543	−1.32308	−0.661539	−	0.749911i	$-0.730096\pi$
$239$	−20.4543	−1.32308	−0.661539	+	0.749911i	$0.730096\pi$
$240$	1.65270	0.106682
$241$	4.61856	0.297507	0.148754	−	0.988874i	$-0.452474\pi$
$241$	4.61856	0.297507	0.148754	+	0.988874i	$0.452474\pi$
$242$	−10.7169	−0.688907
$243$	22.3601	1.43440
$244$	−6.69459	−0.428577
$245$	−0.652704	−0.0416997
$246$	−7.07873	−0.451323
$247$	0	0
$248$	5.59627	0.355363
$249$	−26.9368	−1.70705
$250$	6.24897	0.395220
$251$	−23.4561	−1.48053	−0.740266	−	0.672314i	$-0.765301\pi$
$251$	−23.4561	−1.48053	−0.740266	+	0.672314i	$0.765301\pi$
$252$	3.41147	0.214903
$253$	−4.69459	−0.295147
$254$	−9.72193	−0.610008
$255$	−1.72193	−0.107832
$256$	1.00000	0.0625000
$257$	−21.1070	−1.31662	−0.658309	−	0.752748i	$-0.728728\pi$
$257$	−21.1070	−1.31662	−0.658309	+	0.752748i	$0.728728\pi$
$258$	18.6604	1.16175
$259$	6.90167	0.428849
$260$	−1.22668	−0.0760756
$261$	−16.4270	−1.01680
$262$	10.5398	0.651153
$263$	28.1343	1.73484	0.867419	−	0.497579i	$-0.165777\pi$
$263$	28.1343	1.73484	0.867419	+	0.497579i	$0.165777\pi$
$264$	−1.34730	−0.0829204
$265$	−1.29591	−0.0796072
$266$	0	0
$267$	−31.4097	−1.92224
$268$	3.43107	0.209586
$269$	−4.61081	−0.281126	−0.140563	−	0.990072i	$-0.544891\pi$
$269$	−4.61081	−0.281126	−0.140563	+	0.990072i	$0.544891\pi$
$270$	0.680045	0.0413862
$271$	−3.52023	−0.213839	−0.106919	−	0.994268i	$-0.534099\pi$
$271$	−3.52023	−0.213839	−0.106919	+	0.994268i	$0.534099\pi$
$272$	−1.04189	−0.0631738
$273$	−4.75877	−0.288014
$274$	18.4611	1.11528
$275$	−2.43376	−0.146761
$276$	22.3405	1.34474
$277$	−20.4311	−1.22758	−0.613792	−	0.789468i	$-0.710357\pi$
$277$	−20.4311	−1.22758	−0.613792	+	0.789468i	$0.710357\pi$
$278$	−21.3182	−1.27858
$279$	19.0915	1.14298
$280$	−0.652704	−0.0390065
$281$	11.6304	0.693812	0.346906	−	0.937900i	$-0.387232\pi$
$281$	11.6304	0.693812	0.346906	+	0.937900i	$0.387232\pi$
$282$	1.04189	0.0620436
$283$	−29.3705	−1.74590	−0.872948	−	0.487813i	$-0.837795\pi$
$283$	−29.3705	−1.74590	−0.872948	+	0.487813i	$0.837795\pi$
$284$	−0.554378	−0.0328963
$285$	0	0
$286$	1.00000	0.0591312
$287$	2.79561	0.165019
$288$	3.41147	0.201023
$289$	−15.9145	−0.936145
$290$	3.14290	0.184558
$291$	−13.6459	−0.799937
$292$	0.170245	0.00996281
$293$	31.3901	1.83383	0.916915	−	0.399082i	$-0.130671\pi$
$293$	31.3901	1.83383	0.916915	+	0.399082i	$0.130671\pi$
$294$	−2.53209	−0.147674
$295$	−1.78611	−0.103991
$296$	6.90167	0.401152
$297$	−0.554378	−0.0321683
$298$	9.86484	0.571455
$299$	−16.5817	−0.958946
$300$	11.5817	0.668671
$301$	−7.36959	−0.424776
$302$	2.86484	0.164853
$303$	11.2267	0.644956
$304$	0	0
$305$	4.36959	0.250202
$306$	−3.55438	−0.203190
$307$	−11.7861	−0.672669	−0.336334	−	0.941743i	$-0.609187\pi$
$307$	−11.7861	−0.672669	−0.336334	+	0.941743i	$0.609187\pi$
$308$	0.532089	0.0303186
$309$	47.0137	2.67452
$310$	−3.65270	−0.207460
$311$	23.1634	1.31348	0.656739	−	0.754118i	$-0.271935\pi$
$311$	23.1634	1.31348	0.656739	+	0.754118i	$0.271935\pi$
$312$	−4.75877	−0.269412
$313$	−3.57903	−0.202299	−0.101149	−	0.994871i	$-0.532252\pi$
$313$	−3.57903	−0.202299	−0.101149	+	0.994871i	$0.532252\pi$
$314$	2.39693	0.135266
$315$	−2.22668	−0.125459
$316$	−11.3969	−0.641127
$317$	−7.78787	−0.437410	−0.218705	−	0.975791i	$-0.570183\pi$
$317$	−7.78787	−0.437410	−0.218705	+	0.975791i	$0.570183\pi$
$318$	−5.02734	−0.281919
$319$	−2.56212	−0.143451
$320$	−0.652704	−0.0364872
$321$	−0.630415	−0.0351863
$322$	−8.82295	−0.491684
$323$	0	0
$324$	−7.59627	−0.422015
$325$	−8.59627	−0.476835
$326$	−19.8794	−1.10102
$327$	47.5381	2.62886
$328$	2.79561	0.154362
$329$	−0.411474	−0.0226853
$330$	0.879385	0.0484086
$331$	28.1712	1.54843	0.774214	−	0.632924i	$-0.218145\pi$
$331$	28.1712	1.54843	0.774214	+	0.632924i	$0.218145\pi$
$332$	10.6382	0.583845
$333$	23.5449	1.29025
$334$	9.92127	0.542868
$335$	−2.23947	−0.122356
$336$	−2.53209	−0.138137
$337$	16.5348	0.900707	0.450353	−	0.892850i	$-0.351298\pi$
$337$	16.5348	0.900707	0.450353	+	0.892850i	$0.351298\pi$
$338$	−9.46791	−0.514986
$339$	−13.8084	−0.749969
$340$	0.680045	0.0368806
$341$	2.97771	0.161252
$342$	0	0
$343$	1.00000	0.0539949
$344$	−7.36959	−0.397341
$345$	−14.5817	−0.785053
$346$	−24.9864	−1.34328
$347$	3.65364	0.196138	0.0980688	−	0.995180i	$-0.468733\pi$
$347$	3.65364	0.196138	0.0980688	+	0.995180i	$0.468733\pi$
$348$	12.1925	0.653588
$349$	10.9959	0.588596	0.294298	−	0.955714i	$-0.404914\pi$
$349$	10.9959	0.588596	0.294298	+	0.955714i	$0.404914\pi$
$350$	−4.57398	−0.244489
$351$	−1.95811	−0.104516
$352$	0.532089	0.0283604
$353$	20.3432	1.08276	0.541379	−	0.840779i	$-0.317902\pi$
$353$	20.3432	1.08276	0.541379	+	0.840779i	$0.317902\pi$
$354$	−6.92902	−0.368273
$355$	0.361844	0.0192047
$356$	12.4047	0.657446
$357$	2.63816	0.139626
$358$	−21.6168	−1.14248
$359$	−32.8212	−1.73224	−0.866118	−	0.499839i	$-0.833392\pi$
$359$	−32.8212	−1.73224	−0.866118	+	0.499839i	$0.833392\pi$
$360$	−2.22668	−0.117356
$361$	0	0
$362$	−0.475652	−0.0249997
$363$	27.1361	1.42428
$364$	1.87939	0.0985066
$365$	−0.111119	−0.00581625
$366$	16.9513	0.886059
$367$	32.5577	1.69950	0.849748	−	0.527188i	$-0.176754\pi$
$367$	32.5577	1.69950	0.849748	+	0.527188i	$0.176754\pi$
$368$	−8.82295	−0.459928
$369$	9.53714	0.496484
$370$	−4.50475	−0.234191
$371$	1.98545	0.103080
$372$	−14.1702	−0.734693
$373$	−26.3901	−1.36643	−0.683214	−	0.730218i	$-0.739419\pi$
$373$	−26.3901	−1.36643	−0.683214	+	0.730218i	$0.739419\pi$
$374$	−0.554378	−0.0286662
$375$	−15.8229	−0.817094
$376$	−0.411474	−0.0212202
$377$	−9.04963	−0.466080
$378$	−1.04189	−0.0535890
$379$	−22.3105	−1.14601	−0.573006	−	0.819551i	$-0.694223\pi$
$379$	−22.3105	−1.14601	−0.573006	+	0.819551i	$0.694223\pi$
$380$	0	0
$381$	24.6168	1.26116
$382$	−13.4115	−0.686191
$383$	−20.7879	−1.06221	−0.531105	−	0.847306i	$-0.678223\pi$
$383$	−20.7879	−1.06221	−0.531105	+	0.847306i	$0.678223\pi$
$384$	−2.53209	−0.129215
$385$	−0.347296	−0.0176999
$386$	−10.5466	−0.536810
$387$	−25.1411	−1.27800
$388$	5.38919	0.273594
$389$	4.08553	0.207145	0.103572	−	0.994622i	$-0.466973\pi$
$389$	4.08553	0.207145	0.103572	+	0.994622i	$0.466973\pi$
$390$	3.10607	0.157282
$391$	9.19253	0.464886
$392$	1.00000	0.0505076
$393$	−26.6878	−1.34622
$394$	−10.4483	−0.526378
$395$	7.43882	0.374287
$396$	1.81521	0.0912176
$397$	22.3577	1.12210	0.561051	−	0.827781i	$-0.310397\pi$
$397$	22.3577	1.12210	0.561051	+	0.827781i	$0.310397\pi$
$398$	−12.9804	−0.650649
$399$	0	0
$400$	−4.57398	−0.228699
$401$	−25.2249	−1.25967	−0.629836	−	0.776728i	$-0.716878\pi$
$401$	−25.2249	−1.25967	−0.629836	+	0.776728i	$0.716878\pi$
$402$	−8.68779	−0.433307
$403$	10.5175	0.523916
$404$	−4.43376	−0.220588
$405$	4.95811	0.246371
$406$	−4.81521	−0.238975
$407$	3.67230	0.182029
$408$	2.63816	0.130608
$409$	8.51754	0.421165	0.210583	−	0.977576i	$-0.432464\pi$
$409$	8.51754	0.421165	0.210583	+	0.977576i	$0.432464\pi$
$410$	−1.82470	−0.0901157
$411$	−46.7452	−2.30577
$412$	−18.5672	−0.914739
$413$	2.73648	0.134653
$414$	−30.0993	−1.47930
$415$	−6.94356	−0.340846
$416$	1.87939	0.0921444
$417$	53.9796	2.64339
$418$	0	0
$419$	24.9905	1.22087	0.610433	−	0.792068i	$-0.290995\pi$
$419$	24.9905	1.22087	0.610433	+	0.792068i	$0.290995\pi$
$420$	1.65270	0.0806437
$421$	12.8895	0.628195	0.314098	−	0.949391i	$-0.398298\pi$
$421$	12.8895	0.628195	0.314098	+	0.949391i	$0.398298\pi$
$422$	12.0273	0.585482
$423$	−1.40373	−0.0682519
$424$	1.98545	0.0964221
$425$	4.76558	0.231164
$426$	1.40373	0.0680111
$427$	−6.69459	−0.323974
$428$	0.248970	0.0120344
$429$	−2.53209	−0.122250
$430$	4.81016	0.231966
$431$	2.80747	0.135231	0.0676155	−	0.997711i	$-0.478461\pi$
$431$	2.80747	0.135231	0.0676155	+	0.997711i	$0.478461\pi$
$432$	−1.04189	−0.0501279
$433$	38.8922	1.86904	0.934519	−	0.355912i	$-0.115830\pi$
$433$	38.8922	1.86904	0.934519	+	0.355912i	$0.115830\pi$
$434$	5.59627	0.268629
$435$	−7.95811	−0.381562
$436$	−18.7743	−0.899124
$437$	0	0
$438$	−0.431074	−0.0205975
$439$	−3.38413	−0.161516	−0.0807579	−	0.996734i	$-0.525734\pi$
$439$	−3.38413	−0.161516	−0.0807579	+	0.996734i	$0.525734\pi$
$440$	−0.347296	−0.0165567
$441$	3.41147	0.162451
$442$	−1.95811	−0.0931378
$443$	−6.29355	−0.299015	−0.149508	−	0.988761i	$-0.547769\pi$
$443$	−6.29355	−0.299015	−0.149508	+	0.988761i	$0.547769\pi$
$444$	−17.4757	−0.829358
$445$	−8.09657	−0.383814
$446$	−16.1634	−0.765361
$447$	−24.9786	−1.18145
$448$	1.00000	0.0472456
$449$	4.30541	0.203185	0.101592	−	0.994826i	$-0.467606\pi$
$449$	4.30541	0.203185	0.101592	+	0.994826i	$0.467606\pi$
$450$	−15.6040	−0.735580
$451$	1.48751	0.0700442
$452$	5.45336	0.256505
$453$	−7.25402	−0.340824
$454$	−10.8844	−0.510832
$455$	−1.22668	−0.0575077
$456$	0	0
$457$	8.23711	0.385316	0.192658	−	0.981266i	$-0.438289\pi$
$457$	8.23711	0.385316	0.192658	+	0.981266i	$0.438289\pi$
$458$	−13.3841	−0.625399
$459$	1.08553	0.0506683
$460$	5.75877	0.268504
$461$	−10.0128	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$461$	−10.0128	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$462$	−1.34730	−0.0626819
$463$	36.9127	1.71548	0.857740	−	0.514084i	$-0.171868\pi$
$463$	36.9127	1.71548	0.857740	+	0.514084i	$0.171868\pi$
$464$	−4.81521	−0.223540
$465$	9.24897	0.428911
$466$	19.6432	0.909954
$467$	−35.7178	−1.65282	−0.826412	−	0.563066i	$-0.809622\pi$
$467$	−35.7178	−1.65282	−0.826412	+	0.563066i	$0.809622\pi$
$468$	6.41147	0.296370
$469$	3.43107	0.158432
$470$	0.268571	0.0123882
$471$	−6.06923	−0.279655
$472$	2.73648	0.125957
$473$	−3.92127	−0.180300
$474$	28.8580	1.32549
$475$	0	0
$476$	−1.04189	−0.0477549
$477$	6.77332	0.310129
$478$	−20.4543	−0.935558
$479$	−21.5567	−0.984953	−0.492476	−	0.870326i	$-0.663908\pi$
$479$	−21.5567	−0.984953	−0.492476	+	0.870326i	$0.663908\pi$
$480$	1.65270	0.0754353
$481$	12.9709	0.591422
$482$	4.61856	0.210369
$483$	22.3405	1.01653
$484$	−10.7169	−0.487131
$485$	−3.51754	−0.159723
$486$	22.3601	1.01427
$487$	−20.0223	−0.907297	−0.453648	−	0.891181i	$-0.649878\pi$
$487$	−20.0223	−0.907297	−0.453648	+	0.891181i	$0.649878\pi$
$488$	−6.69459	−0.303050
$489$	50.3364	2.27629
$490$	−0.652704	−0.0294861
$491$	−7.44387	−0.335937	−0.167969	−	0.985792i	$-0.553721\pi$
$491$	−7.44387	−0.335937	−0.167969	+	0.985792i	$0.553721\pi$
$492$	−7.07873	−0.319134
$493$	5.01691	0.225950
$494$	0	0
$495$	−1.18479	−0.0532525
$496$	5.59627	0.251280
$497$	−0.554378	−0.0248672
$498$	−26.9368	−1.20706
$499$	−27.6673	−1.23856	−0.619278	−	0.785172i	$-0.712575\pi$
$499$	−27.6673	−1.23856	−0.619278	+	0.785172i	$0.712575\pi$
$500$	6.24897	0.279462
$501$	−25.1215	−1.12235
$502$	−23.4561	−1.04689
$503$	−39.9213	−1.78000	−0.890001	−	0.455959i	$-0.849296\pi$
$503$	−39.9213	−1.78000	−0.890001	+	0.455959i	$0.849296\pi$
$504$	3.41147	0.151959
$505$	2.89393	0.128778
$506$	−4.69459	−0.208700
$507$	23.9736	1.06470
$508$	−9.72193	−0.431341
$509$	0.997312	0.0442051	0.0221025	−	0.999756i	$-0.492964\pi$
$509$	0.997312	0.0442051	0.0221025	+	0.999756i	$0.492964\pi$
$510$	−1.72193	−0.0762485
$511$	0.170245	0.00753118
$512$	1.00000	0.0441942
$513$	0	0
$514$	−21.1070	−0.930990
$515$	12.1189	0.534021
$516$	18.6604	0.821480
$517$	−0.218941	−0.00962901
$518$	6.90167	0.303242
$519$	63.2677	2.77715
$520$	−1.22668	−0.0537935
$521$	−6.68510	−0.292879	−0.146440	−	0.989220i	$-0.546781\pi$
$521$	−6.68510	−0.292879	−0.146440	+	0.989220i	$0.546781\pi$
$522$	−16.4270	−0.718988
$523$	−22.4679	−0.982453	−0.491227	−	0.871032i	$-0.663451\pi$
$523$	−22.4679	−0.982453	−0.491227	+	0.871032i	$0.663451\pi$
$524$	10.5398	0.460435
$525$	11.5817	0.505468
$526$	28.1343	1.22672
$527$	−5.83069	−0.253989
$528$	−1.34730	−0.0586335
$529$	54.8444	2.38454
$530$	−1.29591	−0.0562908
$531$	9.33544	0.405123
$532$	0	0
$533$	5.25402	0.227577
$534$	−31.4097	−1.35923
$535$	−0.162504	−0.00702565
$536$	3.43107	0.148200
$537$	54.7357	2.36202
$538$	−4.61081	−0.198786
$539$	0.532089	0.0229187
$540$	0.680045	0.0292645
$541$	−12.8922	−0.554278	−0.277139	−	0.960830i	$-0.589386\pi$
$541$	−12.8922	−0.554278	−0.277139	+	0.960830i	$0.589386\pi$
$542$	−3.52023	−0.151207
$543$	1.20439	0.0516854
$544$	−1.04189	−0.0446706
$545$	12.2540	0.524905
$546$	−4.75877	−0.203657
$547$	22.5057	0.962273	0.481137	−	0.876646i	$-0.340224\pi$
$547$	22.5057	0.962273	0.481137	+	0.876646i	$0.340224\pi$
$548$	18.4611	0.788619
$549$	−22.8384	−0.974720
$550$	−2.43376	−0.103776
$551$	0	0
$552$	22.3405	0.950874
$553$	−11.3969	−0.484647
$554$	−20.4311	−0.868033
$555$	11.4064	0.484176
$556$	−21.3182	−0.904093
$557$	−6.50980	−0.275829	−0.137915	−	0.990444i	$-0.544040\pi$
$557$	−6.50980	−0.275829	−0.137915	+	0.990444i	$0.544040\pi$
$558$	19.0915	0.808208
$559$	−13.8503	−0.585805
$560$	−0.652704	−0.0275818
$561$	1.40373	0.0592657
$562$	11.6304	0.490599
$563$	7.29086	0.307273	0.153637	−	0.988127i	$-0.450902\pi$
$563$	7.29086	0.307273	0.153637	+	0.988127i	$0.450902\pi$
$564$	1.04189	0.0438714
$565$	−3.55943	−0.149746
$566$	−29.3705	−1.23453
$567$	−7.59627	−0.319013
$568$	−0.554378	−0.0232612
$569$	−5.31820	−0.222951	−0.111475	−	0.993767i	$-0.535558\pi$
$569$	−5.31820	−0.222951	−0.111475	+	0.993767i	$0.535558\pi$
$570$	0	0
$571$	−43.8408	−1.83468	−0.917340	−	0.398105i	$-0.869668\pi$
$571$	−43.8408	−1.83468	−0.917340	+	0.398105i	$0.869668\pi$
$572$	1.00000	0.0418121
$573$	33.9590	1.41866
$574$	2.79561	0.116686
$575$	40.3560	1.68296
$576$	3.41147	0.142145
$577$	18.7324	0.779838	0.389919	−	0.920849i	$-0.372503\pi$
$577$	18.7324	0.779838	0.389919	+	0.920849i	$0.372503\pi$
$578$	−15.9145	−0.661955
$579$	26.7050	1.10982
$580$	3.14290	0.130502
$581$	10.6382	0.441345
$582$	−13.6459	−0.565641
$583$	1.05644	0.0437531
$584$	0.170245	0.00704477
$585$	−4.18479	−0.173020
$586$	31.3901	1.29671
$587$	24.6869	1.01894	0.509468	−	0.860490i	$-0.329842\pi$
$587$	24.6869	1.01894	0.509468	+	0.860490i	$0.329842\pi$
$588$	−2.53209	−0.104422
$589$	0	0
$590$	−1.78611	−0.0735331
$591$	26.4561	1.08826
$592$	6.90167	0.283657
$593$	−9.47472	−0.389080	−0.194540	−	0.980895i	$-0.562321\pi$
$593$	−9.47472	−0.389080	−0.194540	+	0.980895i	$0.562321\pi$
$594$	−0.554378	−0.0227464
$595$	0.680045	0.0278791
$596$	9.86484	0.404079
$597$	32.8675	1.34518
$598$	−16.5817	−0.678077
$599$	12.7588	0.521309	0.260655	−	0.965432i	$-0.416062\pi$
$599$	12.7588	0.521309	0.260655	+	0.965432i	$0.416062\pi$
$600$	11.5817	0.472822
$601$	25.5422	1.04189	0.520944	−	0.853591i	$-0.325580\pi$
$601$	25.5422	1.04189	0.520944	+	0.853591i	$0.325580\pi$
$602$	−7.36959	−0.300362
$603$	11.7050	0.476665
$604$	2.86484	0.116569
$605$	6.99495	0.284385
$606$	11.2267	0.456053
$607$	−6.75641	−0.274234	−0.137117	−	0.990555i	$-0.543784\pi$
$607$	−6.75641	−0.274234	−0.137117	+	0.990555i	$0.543784\pi$
$608$	0	0
$609$	12.1925	0.494066
$610$	4.36959	0.176919
$611$	−0.773318	−0.0312851
$612$	−3.55438	−0.143677
$613$	−36.7033	−1.48243	−0.741215	−	0.671267i	$-0.765750\pi$
$613$	−36.7033	−1.48243	−0.741215	+	0.671267i	$0.765750\pi$
$614$	−11.7861	−0.475649
$615$	4.62031	0.186309
$616$	0.532089	0.0214385
$617$	17.7196	0.713363	0.356682	−	0.934226i	$-0.383908\pi$
$617$	17.7196	0.713363	0.356682	+	0.934226i	$0.383908\pi$
$618$	47.0137	1.89117
$619$	−24.1411	−0.970315	−0.485157	−	0.874427i	$-0.661238\pi$
$619$	−24.1411	−0.970315	−0.485157	+	0.874427i	$0.661238\pi$
$620$	−3.65270	−0.146696
$621$	9.19253	0.368884
$622$	23.1634	0.928769
$623$	12.4047	0.496982
$624$	−4.75877	−0.190503
$625$	18.7912	0.751647
$626$	−3.57903	−0.143047
$627$	0	0
$628$	2.39693	0.0956478
$629$	−7.19078	−0.286715
$630$	−2.22668	−0.0887131
$631$	23.1411	0.921235	0.460617	−	0.887599i	$-0.347628\pi$
$631$	23.1411	0.921235	0.460617	+	0.887599i	$0.347628\pi$
$632$	−11.3969	−0.453345
$633$	−30.4543	−1.21045
$634$	−7.78787	−0.309296
$635$	6.34554	0.251815
$636$	−5.02734	−0.199347
$637$	1.87939	0.0744640
$638$	−2.56212	−0.101435
$639$	−1.89124	−0.0748165
$640$	−0.652704	−0.0258004
$641$	7.22163	0.285237	0.142619	−	0.989778i	$-0.454448\pi$
$641$	7.22163	0.285237	0.142619	+	0.989778i	$0.454448\pi$
$642$	−0.630415	−0.0248805
$643$	−34.9377	−1.37781	−0.688904	−	0.724853i	$-0.741908\pi$
$643$	−34.9377	−1.37781	−0.688904	+	0.724853i	$0.741908\pi$
$644$	−8.82295	−0.347673
$645$	−12.1797	−0.479577
$646$	0	0
$647$	29.8375	1.17303	0.586517	−	0.809937i	$-0.300499\pi$
$647$	29.8375	1.17303	0.586517	+	0.809937i	$0.300499\pi$
$648$	−7.59627	−0.298410
$649$	1.45605	0.0571550
$650$	−8.59627	−0.337173
$651$	−14.1702	−0.555376
$652$	−19.8794	−0.778537
$653$	25.1803	0.985383	0.492692	−	0.870204i	$-0.336013\pi$
$653$	25.1803	0.985383	0.492692	+	0.870204i	$0.336013\pi$
$654$	47.5381	1.85889
$655$	−6.87939	−0.268800
$656$	2.79561	0.109150
$657$	0.580785	0.0226586
$658$	−0.411474	−0.0160409
$659$	3.46017	0.134789	0.0673945	−	0.997726i	$-0.478531\pi$
$659$	3.46017	0.134789	0.0673945	+	0.997726i	$0.478531\pi$
$660$	0.879385	0.0342300
$661$	−2.20439	−0.0857409	−0.0428705	−	0.999081i	$-0.513650\pi$
$661$	−2.20439	−0.0857409	−0.0428705	+	0.999081i	$0.513650\pi$
$662$	28.1712	1.09490
$663$	4.95811	0.192557
$664$	10.6382	0.412841
$665$	0	0
$666$	23.5449	0.912346
$667$	42.4843	1.64500
$668$	9.92127	0.383866
$669$	40.9273	1.58234
$670$	−2.23947	−0.0865185
$671$	−3.56212	−0.137514
$672$	−2.53209	−0.0976774
$673$	−2.30447	−0.0888309	−0.0444155	−	0.999013i	$-0.514143\pi$
$673$	−2.30447	−0.0888309	−0.0444155	+	0.999013i	$0.514143\pi$
$674$	16.5348	0.636896
$675$	4.76558	0.183427
$676$	−9.46791	−0.364150
$677$	−39.1516	−1.50472	−0.752359	−	0.658754i	$-0.771084\pi$
$677$	−39.1516	−1.50472	−0.752359	+	0.658754i	$0.771084\pi$
$678$	−13.8084	−0.530308
$679$	5.38919	0.206818
$680$	0.680045	0.0260785
$681$	27.5604	1.05612
$682$	2.97771	0.114022
$683$	33.1925	1.27008	0.635038	−	0.772480i	$-0.280984\pi$
$683$	33.1925	1.27008	0.635038	+	0.772480i	$0.280984\pi$
$684$	0	0
$685$	−12.0496	−0.460393
$686$	1.00000	0.0381802
$687$	33.8898	1.29298
$688$	−7.36959	−0.280963
$689$	3.73143	0.142156
$690$	−14.5817	−0.555117
$691$	24.9308	0.948411	0.474206	−	0.880414i	$-0.342735\pi$
$691$	24.9308	0.948411	0.474206	+	0.880414i	$0.342735\pi$
$692$	−24.9864	−0.949840
$693$	1.81521	0.0689540
$694$	3.65364	0.138690
$695$	13.9145	0.527806
$696$	12.1925	0.462157
$697$	−2.91271	−0.110327
$698$	10.9959	0.416200
$699$	−49.7383	−1.88128
$700$	−4.57398	−0.172880
$701$	27.3827	1.03423	0.517115	−	0.855916i	$-0.327006\pi$
$701$	27.3827	1.03423	0.517115	+	0.855916i	$0.327006\pi$
$702$	−1.95811	−0.0739041
$703$	0	0
$704$	0.532089	0.0200539
$705$	−0.680045	−0.0256120
$706$	20.3432	0.765626
$707$	−4.43376	−0.166749
$708$	−6.92902	−0.260408
$709$	−15.7142	−0.590159	−0.295079	−	0.955473i	$-0.595346\pi$
$709$	−15.7142	−0.590159	−0.295079	+	0.955473i	$0.595346\pi$
$710$	0.361844	0.0135798
$711$	−38.8803	−1.45813
$712$	12.4047	0.464885
$713$	−49.3756	−1.84913
$714$	2.63816	0.0987305
$715$	−0.652704	−0.0244097
$716$	−21.6168	−0.807858
$717$	51.7921	1.93421
$718$	−32.8212	−1.22488
$719$	−42.2927	−1.57725	−0.788626	−	0.614873i	$-0.789207\pi$
$719$	−42.2927	−1.57725	−0.788626	+	0.614873i	$0.789207\pi$
$720$	−2.22668	−0.0829835
$721$	−18.5672	−0.691478
$722$	0	0
$723$	−11.6946	−0.434927
$724$	−0.475652	−0.0176775
$725$	22.0247	0.817975
$726$	27.1361	1.00711
$727$	−36.9641	−1.37092	−0.685461	−	0.728109i	$-0.740399\pi$
$727$	−36.9641	−1.37092	−0.685461	+	0.728109i	$0.740399\pi$
$728$	1.87939	0.0696547
$729$	−33.8289	−1.25292
$730$	−0.111119	−0.00411271
$731$	7.67829	0.283992
$732$	16.9513	0.626538
$733$	−35.7461	−1.32031	−0.660156	−	0.751129i	$-0.729510\pi$
$733$	−35.7461	−1.32031	−0.660156	+	0.751129i	$0.729510\pi$
$734$	32.5577	1.20173
$735$	1.65270	0.0609609
$736$	−8.82295	−0.325218
$737$	1.82564	0.0672482
$738$	9.53714	0.351067
$739$	−20.1233	−0.740248	−0.370124	−	0.928982i	$-0.620685\pi$
$739$	−20.1233	−0.740248	−0.370124	+	0.928982i	$0.620685\pi$
$740$	−4.50475	−0.165598
$741$	0	0
$742$	1.98545	0.0728882
$743$	39.7324	1.45764	0.728820	−	0.684706i	$-0.240069\pi$
$743$	39.7324	1.45764	0.728820	+	0.684706i	$0.240069\pi$
$744$	−14.1702	−0.519506
$745$	−6.43882	−0.235900
$746$	−26.3901	−0.966211
$747$	36.2918	1.32785
$748$	−0.554378	−0.0202701
$749$	0.248970	0.00909718
$750$	−15.8229	−0.577772
$751$	38.6705	1.41111	0.705554	−	0.708656i	$-0.250698\pi$
$751$	38.6705	1.41111	0.705554	+	0.708656i	$0.250698\pi$
$752$	−0.411474	−0.0150049
$753$	59.3928	2.16439
$754$	−9.04963	−0.329568
$755$	−1.86989	−0.0680523
$756$	−1.04189	−0.0378931
$757$	8.57222	0.311563	0.155781	−	0.987792i	$-0.450210\pi$
$757$	8.57222	0.311563	0.155781	+	0.987792i	$0.450210\pi$
$758$	−22.3105	−0.810352
$759$	11.8871	0.431475
$760$	0	0
$761$	17.1598	0.622043	0.311021	−	0.950403i	$-0.399329\pi$
$761$	17.1598	0.622043	0.311021	+	0.950403i	$0.399329\pi$
$762$	24.6168	0.891773
$763$	−18.7743	−0.679674
$764$	−13.4115	−0.485210
$765$	2.31996	0.0838782
$766$	−20.7879	−0.751096
$767$	5.14290	0.185699
$768$	−2.53209	−0.0913689
$769$	−6.58441	−0.237440	−0.118720	−	0.992928i	$-0.537879\pi$
$769$	−6.58441	−0.237440	−0.118720	+	0.992928i	$0.537879\pi$
$770$	−0.347296	−0.0125157
$771$	53.4448	1.92477
$772$	−10.5466	−0.379582
$773$	−20.3773	−0.732921	−0.366461	−	0.930434i	$-0.619431\pi$
$773$	−20.3773	−0.732921	−0.366461	+	0.930434i	$0.619431\pi$
$774$	−25.1411	−0.903680
$775$	−25.5972	−0.919479
$776$	5.38919	0.193460
$777$	−17.4757	−0.626936
$778$	4.08553	0.146473
$779$	0	0
$780$	3.10607	0.111215
$781$	−0.294978	−0.0105551
$782$	9.19253	0.328724
$783$	5.01691	0.179290
$784$	1.00000	0.0357143
$785$	−1.56448	−0.0558388
$786$	−26.6878	−0.951922
$787$	11.4074	0.406628	0.203314	−	0.979114i	$-0.434829\pi$
$787$	11.4074	0.406628	0.203314	+	0.979114i	$0.434829\pi$
$788$	−10.4483	−0.372206
$789$	−71.2387	−2.53616
$790$	7.43882	0.264661
$791$	5.45336	0.193899
$792$	1.81521	0.0645006
$793$	−12.5817	−0.446790
$794$	22.3577	0.793446
$795$	3.28136	0.116378
$796$	−12.9804	−0.460078
$797$	48.7743	1.72767	0.863836	−	0.503773i	$-0.168055\pi$
$797$	48.7743	1.72767	0.863836	+	0.503773i	$0.168055\pi$
$798$	0	0
$799$	0.428710	0.0151667
$800$	−4.57398	−0.161715
$801$	42.3182	1.49524
$802$	−25.2249	−0.890723
$803$	0.0905853	0.00319668
$804$	−8.68779	−0.306395
$805$	5.75877	0.202970
$806$	10.5175	0.370465
$807$	11.6750	0.410979
$808$	−4.43376	−0.155979
$809$	−36.5003	−1.28328	−0.641641	−	0.767005i	$-0.721746\pi$
$809$	−36.5003	−1.28328	−0.641641	+	0.767005i	$0.721746\pi$
$810$	4.95811	0.174210
$811$	−46.5850	−1.63582	−0.817911	−	0.575345i	$-0.804868\pi$
$811$	−46.5850	−1.63582	−0.817911	+	0.575345i	$0.804868\pi$
$812$	−4.81521	−0.168981
$813$	8.91353	0.312611
$814$	3.67230	0.128714
$815$	12.9753	0.454507
$816$	2.63816	0.0923539
$817$	0	0
$818$	8.51754	0.297809
$819$	6.41147	0.224035
$820$	−1.82470	−0.0637214
$821$	−18.0024	−0.628287	−0.314143	−	0.949376i	$-0.601717\pi$
$821$	−18.0024	−0.628287	−0.314143	+	0.949376i	$0.601717\pi$
$822$	−46.7452	−1.63042
$823$	−15.0746	−0.525468	−0.262734	−	0.964868i	$-0.584624\pi$
$823$	−15.0746	−0.525468	−0.262734	+	0.964868i	$0.584624\pi$
$824$	−18.5672	−0.646818
$825$	6.16250	0.214551
$826$	2.73648	0.0952144
$827$	−33.5327	−1.16605	−0.583023	−	0.812456i	$-0.698130\pi$
$827$	−33.5327	−1.16605	−0.583023	+	0.812456i	$0.698130\pi$
$828$	−30.0993	−1.04602
$829$	30.1539	1.04729	0.523645	−	0.851937i	$-0.324572\pi$
$829$	30.1539	1.04729	0.523645	+	0.851937i	$0.324572\pi$
$830$	−6.94356	−0.241015
$831$	51.7333	1.79461
$832$	1.87939	0.0651560
$833$	−1.04189	−0.0360993
$834$	53.9796	1.86916
$835$	−6.47565	−0.224099
$836$	0	0
$837$	−5.83069	−0.201538
$838$	24.9905	0.863283
$839$	40.6979	1.40505	0.702524	−	0.711660i	$-0.252057\pi$
$839$	40.6979	1.40505	0.702524	+	0.711660i	$0.252057\pi$
$840$	1.65270	0.0570237
$841$	−5.81378	−0.200475
$842$	12.8895	0.444201
$843$	−29.4492	−1.01429
$844$	12.0273	0.413998
$845$	6.17974	0.212590
$846$	−1.40373	−0.0482613
$847$	−10.7169	−0.368236
$848$	1.98545	0.0681807
$849$	74.3688	2.55233
$850$	4.76558	0.163458
$851$	−60.8931	−2.08739
$852$	1.40373	0.0480911
$853$	9.64227	0.330145	0.165073	−	0.986281i	$-0.447214\pi$
$853$	9.64227	0.330145	0.165073	+	0.986281i	$0.447214\pi$
$854$	−6.69459	−0.229084
$855$	0	0
$856$	0.248970	0.00850963
$857$	56.6008	1.93345	0.966724	−	0.255823i	$-0.0823464\pi$
$857$	56.6008	1.93345	0.966724	+	0.255823i	$0.0823464\pi$
$858$	−2.53209	−0.0864441
$859$	21.0770	0.719137	0.359568	−	0.933119i	$-0.382924\pi$
$859$	21.0770	0.719137	0.359568	+	0.933119i	$0.382924\pi$
$860$	4.81016	0.164025
$861$	−7.07873	−0.241242
$862$	2.80747	0.0956227
$863$	−36.9513	−1.25784	−0.628919	−	0.777471i	$-0.716502\pi$
$863$	−36.9513	−1.25784	−0.628919	+	0.777471i	$0.716502\pi$
$864$	−1.04189	−0.0354458
$865$	16.3087	0.554513
$866$	38.8922	1.32161
$867$	40.2968	1.36855
$868$	5.59627	0.189950
$869$	−6.06418	−0.205713
$870$	−7.95811	−0.269805
$871$	6.44831	0.218493
$872$	−18.7743	−0.635776
$873$	18.3851	0.622240
$874$	0	0
$875$	6.24897	0.211254
$876$	−0.431074	−0.0145647
$877$	−4.30304	−0.145303	−0.0726517	−	0.997357i	$-0.523146\pi$
$877$	−4.30304	−0.145303	−0.0726517	+	0.997357i	$0.523146\pi$
$878$	−3.38413	−0.114209
$879$	−79.4826	−2.68088
$880$	−0.347296	−0.0117074
$881$	3.37464	0.113694	0.0568472	−	0.998383i	$-0.481895\pi$
$881$	3.37464	0.113694	0.0568472	+	0.998383i	$0.481895\pi$
$882$	3.41147	0.114870
$883$	30.2995	1.01966	0.509830	−	0.860275i	$-0.329708\pi$
$883$	30.2995	1.01966	0.509830	+	0.860275i	$0.329708\pi$
$884$	−1.95811	−0.0658584
$885$	4.52259	0.152025
$886$	−6.29355	−0.211436
$887$	51.3046	1.72264	0.861320	−	0.508063i	$-0.169638\pi$
$887$	51.3046	1.72264	0.861320	+	0.508063i	$0.169638\pi$
$888$	−17.4757	−0.586444
$889$	−9.72193	−0.326063
$890$	−8.09657	−0.271398
$891$	−4.04189	−0.135408
$892$	−16.1634	−0.541192
$893$	0	0
$894$	−24.9786	−0.835411
$895$	14.1094	0.471624
$896$	1.00000	0.0334077
$897$	41.9864	1.40188
$898$	4.30541	0.143673
$899$	−26.9472	−0.898739
$900$	−15.6040	−0.520134
$901$	−2.06862	−0.0689158
$902$	1.48751	0.0495287
$903$	18.6604	0.620981
$904$	5.45336	0.181376
$905$	0.310460	0.0103200
$906$	−7.25402	−0.240999
$907$	20.5071	0.680927	0.340464	−	0.940258i	$-0.389416\pi$
$907$	20.5071	0.680927	0.340464	+	0.940258i	$0.389416\pi$
$908$	−10.8844	−0.361213
$909$	−15.1257	−0.501687
$910$	−1.22668	−0.0406641
$911$	−10.6227	−0.351945	−0.175972	−	0.984395i	$-0.556307\pi$
$911$	−10.6227	−0.351945	−0.175972	+	0.984395i	$0.556307\pi$
$912$	0	0
$913$	5.66044	0.187333
$914$	8.23711	0.272459
$915$	−11.0642	−0.365770
$916$	−13.3841	−0.442224
$917$	10.5398	0.348056
$918$	1.08553	0.0358279
$919$	−0.552014	−0.0182092	−0.00910462	−	0.999959i	$-0.502898\pi$
$919$	−0.552014	−0.0182092	−0.00910462	+	0.999959i	$0.502898\pi$
$920$	5.75877	0.189861
$921$	29.8435	0.983376
$922$	−10.0128	−0.329754
$923$	−1.04189	−0.0342942
$924$	−1.34730	−0.0443228
$925$	−31.5681	−1.03795
$926$	36.9127	1.21303
$927$	−63.3414	−2.08041
$928$	−4.81521	−0.158067
$929$	55.3292	1.81529	0.907647	−	0.419735i	$-0.137877\pi$
$929$	55.3292	1.81529	0.907647	+	0.419735i	$0.137877\pi$
$930$	9.24897	0.303286
$931$	0	0
$932$	19.6432	0.643435
$933$	−58.6519	−1.92018
$934$	−35.7178	−1.16872
$935$	0.361844	0.0118336
$936$	6.41147	0.209566
$937$	5.48339	0.179135	0.0895673	−	0.995981i	$-0.471452\pi$
$937$	5.48339	0.179135	0.0895673	+	0.995981i	$0.471452\pi$
$938$	3.43107	0.112029
$939$	9.06242	0.295741
$940$	0.268571	0.00875981
$941$	−47.1239	−1.53620	−0.768098	−	0.640333i	$-0.778797\pi$
$941$	−47.1239	−1.53620	−0.768098	+	0.640333i	$0.778797\pi$
$942$	−6.06923	−0.197746
$943$	−24.6655	−0.803219
$944$	2.73648	0.0890649
$945$	0.680045	0.0221219
$946$	−3.92127	−0.127492
$947$	29.7134	0.965555	0.482777	−	0.875743i	$-0.339628\pi$
$947$	29.7134	0.965555	0.482777	+	0.875743i	$0.339628\pi$
$948$	28.8580	0.937265
$949$	0.319955	0.0103862
$950$	0	0
$951$	19.7196	0.639451
$952$	−1.04189	−0.0337678
$953$	34.9804	1.13313	0.566563	−	0.824018i	$-0.308273\pi$
$953$	34.9804	1.13313	0.566563	+	0.824018i	$0.308273\pi$
$954$	6.77332	0.219294
$955$	8.75372	0.283264
$956$	−20.4543	−0.661539
$957$	6.48751	0.209711
$958$	−21.5567	−0.696467
$959$	18.4611	0.596140
$960$	1.65270	0.0533408
$961$	0.318201	0.0102645
$962$	12.9709	0.418199
$963$	0.849356	0.0273701
$964$	4.61856	0.148754
$965$	6.88383	0.221598
$966$	22.3405	0.718793
$967$	−27.8462	−0.895472	−0.447736	−	0.894166i	$-0.647770\pi$
$967$	−27.8462	−0.895472	−0.447736	+	0.894166i	$0.647770\pi$
$968$	−10.7169	−0.344454
$969$	0	0
$970$	−3.51754	−0.112941
$971$	14.5226	0.466052	0.233026	−	0.972470i	$-0.425137\pi$
$971$	14.5226	0.466052	0.233026	+	0.972470i	$0.425137\pi$
$972$	22.3601	0.717200
$973$	−21.3182	−0.683430
$974$	−20.0223	−0.641556
$975$	21.7665	0.697086
$976$	−6.69459	−0.214289
$977$	−3.93676	−0.125948	−0.0629740	−	0.998015i	$-0.520059\pi$
$977$	−3.93676	−0.125948	−0.0629740	+	0.998015i	$0.520059\pi$
$978$	50.3364	1.60958
$979$	6.60039	0.210949
$980$	−0.652704	−0.0208499
$981$	−64.0479	−2.04489
$982$	−7.44387	−0.237543
$983$	−47.1898	−1.50512	−0.752561	−	0.658522i	$-0.771182\pi$
$983$	−47.1898	−1.50512	−0.752561	+	0.658522i	$0.771182\pi$
$984$	−7.07873	−0.225662
$985$	6.81965	0.217292
$986$	5.01691	0.159771
$987$	1.04189	0.0331637
$988$	0	0
$989$	65.0215	2.06756
$990$	−1.18479	−0.0376552
$991$	−7.51754	−0.238803	−0.119401	−	0.992846i	$-0.538097\pi$
$991$	−7.51754	−0.238803	−0.119401	+	0.992846i	$0.538097\pi$
$992$	5.59627	0.177682
$993$	−71.3319	−2.26365
$994$	−0.554378	−0.0175838
$995$	8.47235	0.268592
$996$	−26.9368	−0.853524
$997$	18.0743	0.572418	0.286209	−	0.958167i	$-0.407605\pi$
$997$	18.0743	0.572418	0.286209	+	0.958167i	$0.407605\pi$
$998$	−27.6673	−0.875792
$999$	−7.19078	−0.227506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.t.1.1		3
19.4	even	9		266.2.u.a.225.1	✓	6
19.5	even	9		266.2.u.a.253.1	yes	6
19.18	odd	2		5054.2.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.a.225.1	✓	6	19.4	even	9
266.2.u.a.253.1	yes	6	19.5	even	9
5054.2.a.s.1.3		3	19.18	odd	2
5054.2.a.t.1.1		3	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.53209 q^{3} +1.00000 q^{4} -0.652704 q^{5} -2.53209 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.41147 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.53209 q^{3} +1.00000 q^{4} -0.652704 q^{5} -2.53209 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.41147 q^{9} -0.652704 q^{10} +0.532089 q^{11} -2.53209 q^{12} +1.87939 q^{13} +1.00000 q^{14} +1.65270 q^{15} +1.00000 q^{16} -1.04189 q^{17} +3.41147 q^{18} -0.652704 q^{20} -2.53209 q^{21} +0.532089 q^{22} -8.82295 q^{23} -2.53209 q^{24} -4.57398 q^{25} +1.87939 q^{26} -1.04189 q^{27} +1.00000 q^{28} -4.81521 q^{29} +1.65270 q^{30} +5.59627 q^{31} +1.00000 q^{32} -1.34730 q^{33} -1.04189 q^{34} -0.652704 q^{35} +3.41147 q^{36} +6.90167 q^{37} -4.75877 q^{39} -0.652704 q^{40} +2.79561 q^{41} -2.53209 q^{42} -7.36959 q^{43} +0.532089 q^{44} -2.22668 q^{45} -8.82295 q^{46} -0.411474 q^{47} -2.53209 q^{48} +1.00000 q^{49} -4.57398 q^{50} +2.63816 q^{51} +1.87939 q^{52} +1.98545 q^{53} -1.04189 q^{54} -0.347296 q^{55} +1.00000 q^{56} -4.81521 q^{58} +2.73648 q^{59} +1.65270 q^{60} -6.69459 q^{61} +5.59627 q^{62} +3.41147 q^{63} +1.00000 q^{64} -1.22668 q^{65} -1.34730 q^{66} +3.43107 q^{67} -1.04189 q^{68} +22.3405 q^{69} -0.652704 q^{70} -0.554378 q^{71} +3.41147 q^{72} +0.170245 q^{73} +6.90167 q^{74} +11.5817 q^{75} +0.532089 q^{77} -4.75877 q^{78} -11.3969 q^{79} -0.652704 q^{80} -7.59627 q^{81} +2.79561 q^{82} +10.6382 q^{83} -2.53209 q^{84} +0.680045 q^{85} -7.36959 q^{86} +12.1925 q^{87} +0.532089 q^{88} +12.4047 q^{89} -2.22668 q^{90} +1.87939 q^{91} -8.82295 q^{92} -14.1702 q^{93} -0.411474 q^{94} -2.53209 q^{96} +5.38919 q^{97} +1.00000 q^{98} +1.81521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 3 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} - 6 q^{46} + 9 q^{47} - 3 q^{48} + 3 q^{49} - 6 q^{50} - 9 q^{51} - 12 q^{53} + 3 q^{56} - 18 q^{58} + 3 q^{59} + 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} + 3 q^{65} - 3 q^{66} + 3 q^{67} + 24 q^{69} - 3 q^{70} + 9 q^{71} - 21 q^{73} + 9 q^{74} + 3 q^{75} - 3 q^{77} - 3 q^{78} - 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} - 3 q^{84} - 18 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} - 15 q^{89} - 6 q^{92} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 12 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 3 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 - 6 * q^46 + 9 * q^47 - 3 * q^48 + 3 * q^49 - 6 * q^50 - 9 * q^51 - 12 * q^53 + 3 * q^56 - 18 * q^58 + 3 * q^59 + 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 + 3 * q^65 - 3 * q^66 + 3 * q^67 + 24 * q^69 - 3 * q^70 + 9 * q^71 - 21 * q^73 + 9 * q^74 + 3 * q^75 - 3 * q^77 - 3 * q^78 - 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 - 3 * q^84 - 18 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 - 15 * q^89 - 6 * q^92 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 12 * q^97 + 3 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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