LMFDB - Embedded newform 5054.2.a.bl.1.7

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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.7
Root			$-0.0101006$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0101006 q^{3} +1.00000 q^{4} -3.08958 q^{5} -0.0101006 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99990 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0101006 q^{3} +1.00000 q^{4} -3.08958 q^{5} -0.0101006 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99990 q^{9} +3.08958 q^{10} -6.48034 q^{11} +0.0101006 q^{12} -1.04019 q^{13} -1.00000 q^{14} -0.0312065 q^{15} +1.00000 q^{16} +2.51415 q^{17} +2.99990 q^{18} -3.08958 q^{20} +0.0101006 q^{21} +6.48034 q^{22} -8.22045 q^{23} -0.0101006 q^{24} +4.54553 q^{25} +1.04019 q^{26} -0.0606024 q^{27} +1.00000 q^{28} -5.21995 q^{29} +0.0312065 q^{30} -8.22208 q^{31} -1.00000 q^{32} -0.0654551 q^{33} -2.51415 q^{34} -3.08958 q^{35} -2.99990 q^{36} -3.78473 q^{37} -0.0105065 q^{39} +3.08958 q^{40} +6.35887 q^{41} -0.0101006 q^{42} +1.33133 q^{43} -6.48034 q^{44} +9.26844 q^{45} +8.22045 q^{46} -2.96047 q^{47} +0.0101006 q^{48} +1.00000 q^{49} -4.54553 q^{50} +0.0253944 q^{51} -1.04019 q^{52} +0.538413 q^{53} +0.0606024 q^{54} +20.0216 q^{55} -1.00000 q^{56} +5.21995 q^{58} -11.1502 q^{59} -0.0312065 q^{60} -8.50062 q^{61} +8.22208 q^{62} -2.99990 q^{63} +1.00000 q^{64} +3.21376 q^{65} +0.0654551 q^{66} -12.4021 q^{67} +2.51415 q^{68} -0.0830312 q^{69} +3.08958 q^{70} -4.19018 q^{71} +2.99990 q^{72} +10.6965 q^{73} +3.78473 q^{74} +0.0459124 q^{75} -6.48034 q^{77} +0.0105065 q^{78} -10.7217 q^{79} -3.08958 q^{80} +8.99908 q^{81} -6.35887 q^{82} -6.72185 q^{83} +0.0101006 q^{84} -7.76769 q^{85} -1.33133 q^{86} -0.0527245 q^{87} +6.48034 q^{88} -2.05416 q^{89} -9.26844 q^{90} -1.04019 q^{91} -8.22045 q^{92} -0.0830477 q^{93} +2.96047 q^{94} -0.0101006 q^{96} +18.9122 q^{97} -1.00000 q^{98} +19.4404 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * 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
$3$	0.0101006	0.00583156	0.00291578	−	0.999996i	$-0.499072\pi$
$3$	0.0101006	0.00583156	0.00291578	+	0.999996i	$0.499072\pi$
$4$	1.00000	0.500000
$5$	−3.08958	−1.38170	−0.690852	−	0.722996i	$-0.742764\pi$
$5$	−3.08958	−1.38170	−0.690852	+	0.722996i	$0.742764\pi$
$6$	−0.0101006	−0.00412354
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.99990	−0.999966
$10$	3.08958	0.977012
$11$	−6.48034	−1.95390	−0.976948	−	0.213476i	$-0.931521\pi$
$11$	−6.48034	−1.95390	−0.976948	+	0.213476i	$0.931521\pi$
$12$	0.0101006	0.00291578
$13$	−1.04019	−0.288497	−0.144249	−	0.989541i	$-0.546076\pi$
$13$	−1.04019	−0.288497	−0.144249	+	0.989541i	$0.546076\pi$
$14$	−1.00000	−0.267261
$15$	−0.0312065	−0.00805749
$16$	1.00000	0.250000
$17$	2.51415	0.609772	0.304886	−	0.952389i	$-0.401382\pi$
$17$	2.51415	0.609772	0.304886	+	0.952389i	$0.401382\pi$
$18$	2.99990	0.707083
$19$	0	0
$19$	0	0
$20$	−3.08958	−0.690852
$21$	0.0101006	0.00220412
$22$	6.48034	1.38161
$23$	−8.22045	−1.71408	−0.857042	−	0.515247i	$-0.827700\pi$
$23$	−8.22045	−1.71408	−0.857042	+	0.515247i	$0.827700\pi$
$24$	−0.0101006	−0.00206177
$25$	4.54553	0.909106
$26$	1.04019	0.203998
$27$	−0.0606024	−0.0116629
$28$	1.00000	0.188982
$29$	−5.21995	−0.969321	−0.484661	−	0.874702i	$-0.661057\pi$
$29$	−5.21995	−0.969321	−0.484661	+	0.874702i	$0.661057\pi$
$30$	0.0312065	0.00569751
$31$	−8.22208	−1.47673	−0.738365	−	0.674402i	$-0.764402\pi$
$31$	−8.22208	−1.47673	−0.738365	+	0.674402i	$0.764402\pi$
$32$	−1.00000	−0.176777
$33$	−0.0654551	−0.0113943
$34$	−2.51415	−0.431174
$35$	−3.08958	−0.522235
$36$	−2.99990	−0.499983
$37$	−3.78473	−0.622206	−0.311103	−	0.950376i	$-0.600698\pi$
$37$	−3.78473	−0.622206	−0.311103	+	0.950376i	$0.600698\pi$
$38$	0	0
$39$	−0.0105065	−0.00168239
$40$	3.08958	0.488506
$41$	6.35887	0.993089	0.496544	−	0.868011i	$-0.334602\pi$
$41$	6.35887	0.993089	0.496544	+	0.868011i	$0.334602\pi$
$42$	−0.0101006	−0.00155855
$43$	1.33133	0.203026	0.101513	−	0.994834i	$-0.467632\pi$
$43$	1.33133	0.203026	0.101513	+	0.994834i	$0.467632\pi$
$44$	−6.48034	−0.976948
$45$	9.26844	1.38166
$46$	8.22045	1.21204
$47$	−2.96047	−0.431829	−0.215915	−	0.976412i	$-0.569273\pi$
$47$	−2.96047	−0.431829	−0.215915	+	0.976412i	$0.569273\pi$
$48$	0.0101006	0.00145789
$49$	1.00000	0.142857
$50$	−4.54553	−0.642835
$51$	0.0253944	0.00355592
$52$	−1.04019	−0.144249
$53$	0.538413	0.0739568	0.0369784	−	0.999316i	$-0.488227\pi$
$53$	0.538413	0.0739568	0.0369784	+	0.999316i	$0.488227\pi$
$54$	0.0606024	0.00824694
$55$	20.0216	2.69971
$56$	−1.00000	−0.133631
$57$	0	0
$58$	5.21995	0.685413
$59$	−11.1502	−1.45163	−0.725816	−	0.687889i	$-0.758537\pi$
$59$	−11.1502	−1.45163	−0.725816	+	0.687889i	$0.758537\pi$
$60$	−0.0312065	−0.00402875
$61$	−8.50062	−1.08839	−0.544196	−	0.838958i	$-0.683165\pi$
$61$	−8.50062	−1.08839	−0.544196	+	0.838958i	$0.683165\pi$
$62$	8.22208	1.04421
$63$	−2.99990	−0.377952
$64$	1.00000	0.125000
$65$	3.21376	0.398618
$66$	0.0654551	0.00805697
$67$	−12.4021	−1.51515	−0.757576	−	0.652747i	$-0.773617\pi$
$67$	−12.4021	−1.51515	−0.757576	+	0.652747i	$0.773617\pi$
$68$	2.51415	0.304886
$69$	−0.0830312	−0.00999579
$70$	3.08958	0.369276
$71$	−4.19018	−0.497283	−0.248641	−	0.968596i	$-0.579984\pi$
$71$	−4.19018	−0.497283	−0.248641	+	0.968596i	$0.579984\pi$
$72$	2.99990	0.353541
$73$	10.6965	1.25193	0.625964	−	0.779852i	$-0.284706\pi$
$73$	10.6965	1.25193	0.625964	+	0.779852i	$0.284706\pi$
$74$	3.78473	0.439966
$75$	0.0459124	0.00530151
$76$	0	0
$77$	−6.48034	−0.738503
$78$	0.0105065	0.00118963
$79$	−10.7217	−1.20629	−0.603143	−	0.797633i	$-0.706085\pi$
$79$	−10.7217	−1.20629	−0.603143	+	0.797633i	$0.706085\pi$
$80$	−3.08958	−0.345426
$81$	8.99908	0.999898
$82$	−6.35887	−0.702220
$83$	−6.72185	−0.737819	−0.368910	−	0.929465i	$-0.620269\pi$
$83$	−6.72185	−0.737819	−0.368910	+	0.929465i	$0.620269\pi$
$84$	0.0101006	0.00110206
$85$	−7.76769	−0.842524
$86$	−1.33133	−0.143561
$87$	−0.0527245	−0.00565266
$88$	6.48034	0.690807
$89$	−2.05416	−0.217741	−0.108871	−	0.994056i	$-0.534723\pi$
$89$	−2.05416	−0.217741	−0.108871	+	0.994056i	$0.534723\pi$
$90$	−9.26844	−0.976979
$91$	−1.04019	−0.109042
$92$	−8.22045	−0.857042
$93$	−0.0830477	−0.00861164
$94$	2.96047	0.305349
$95$	0	0
$96$	−0.0101006	−0.00103088
$97$	18.9122	1.92024	0.960122	−	0.279581i	$-0.0901956\pi$
$97$	18.9122	1.92024	0.960122	+	0.279581i	$0.0901956\pi$
$98$	−1.00000	−0.101015
$99$	19.4404	1.95383
$100$	4.54553	0.454553
$101$	−6.26894	−0.623783	−0.311892	−	0.950118i	$-0.600963\pi$
$101$	−6.26894	−0.623783	−0.311892	+	0.950118i	$0.600963\pi$
$102$	−0.0253944	−0.00251442
$103$	−9.62321	−0.948203	−0.474102	−	0.880470i	$-0.657227\pi$
$103$	−9.62321	−0.948203	−0.474102	+	0.880470i	$0.657227\pi$
$104$	1.04019	0.101999
$105$	−0.0312065	−0.00304545
$106$	−0.538413	−0.0522953
$107$	3.50365	0.338710	0.169355	−	0.985555i	$-0.445831\pi$
$107$	3.50365	0.338710	0.169355	+	0.985555i	$0.445831\pi$
$108$	−0.0606024	−0.00583146
$109$	−6.32193	−0.605531	−0.302766	−	0.953065i	$-0.597910\pi$
$109$	−6.32193	−0.605531	−0.302766	+	0.953065i	$0.597910\pi$
$110$	−20.0216	−1.90898
$111$	−0.0382279	−0.00362843
$112$	1.00000	0.0944911
$113$	−9.17404	−0.863021	−0.431511	−	0.902108i	$-0.642019\pi$
$113$	−9.17404	−0.863021	−0.431511	+	0.902108i	$0.642019\pi$
$114$	0	0
$115$	25.3978	2.36836
$116$	−5.21995	−0.484661
$117$	3.12047	0.288487
$118$	11.1502	1.02646
$119$	2.51415	0.230472
$120$	0.0312065	0.00284875
$121$	30.9948	2.81771
$122$	8.50062	0.769610
$123$	0.0642282	0.00579126
$124$	−8.22208	−0.738365
$125$	1.40413	0.125589
$126$	2.99990	0.267252
$127$	15.2907	1.35683	0.678416	−	0.734678i	$-0.262667\pi$
$127$	15.2907	1.35683	0.678416	+	0.734678i	$0.262667\pi$
$128$	−1.00000	−0.0883883
$129$	0.0134472	0.00118396
$130$	−3.21376	−0.281865
$131$	11.9591	1.04487	0.522436	−	0.852679i	$-0.325023\pi$
$131$	11.9591	1.04487	0.522436	+	0.852679i	$0.325023\pi$
$132$	−0.0654551	−0.00569714
$133$	0	0
$134$	12.4021	1.07137
$135$	0.187236	0.0161147
$136$	−2.51415	−0.215587
$137$	−2.02231	−0.172778	−0.0863889	−	0.996261i	$-0.527533\pi$
$137$	−2.02231	−0.172778	−0.0863889	+	0.996261i	$0.527533\pi$
$138$	0.0830312	0.00706809
$139$	3.30573	0.280388	0.140194	−	0.990124i	$-0.455227\pi$
$139$	3.30573	0.280388	0.140194	+	0.990124i	$0.455227\pi$
$140$	−3.08958	−0.261117
$141$	−0.0299024	−0.00251824
$142$	4.19018	0.351632
$143$	6.74079	0.563694
$144$	−2.99990	−0.249991
$145$	16.1275	1.33931
$146$	−10.6965	−0.885246
$147$	0.0101006	0.000833081 0
$148$	−3.78473	−0.311103
$149$	−2.78517	−0.228170	−0.114085	−	0.993471i	$-0.536394\pi$
$149$	−2.78517	−0.228170	−0.114085	+	0.993471i	$0.536394\pi$
$150$	−0.0459124	−0.00374873
$151$	−13.5357	−1.10152	−0.550759	−	0.834664i	$-0.685662\pi$
$151$	−13.5357	−1.10152	−0.550759	+	0.834664i	$0.685662\pi$
$152$	0	0
$153$	−7.54220	−0.609751
$154$	6.48034	0.522201
$155$	25.4028	2.04040
$156$	−0.0105065	−0.000841195 0
$157$	3.10988	0.248196	0.124098	−	0.992270i	$-0.460396\pi$
$157$	3.10988	0.248196	0.124098	+	0.992270i	$0.460396\pi$
$158$	10.7217	0.852973
$159$	0.00543828	0.000431284 0
$160$	3.08958	0.244253
$161$	−8.22045	−0.647862
$162$	−8.99908	−0.707035
$163$	17.4728	1.36858	0.684289	−	0.729211i	$-0.260113\pi$
$163$	17.4728	1.36858	0.684289	+	0.729211i	$0.260113\pi$
$164$	6.35887	0.496544
$165$	0.202229	0.0157435
$166$	6.72185	0.521717
$167$	19.3247	1.49539	0.747694	−	0.664044i	$-0.231161\pi$
$167$	19.3247	1.49539	0.747694	+	0.664044i	$0.231161\pi$
$168$	−0.0101006	−0.000779276 0
$169$	−11.9180	−0.916769
$170$	7.76769	0.595754
$171$	0	0
$172$	1.33133	0.101513
$173$	−25.1904	−1.91519	−0.957597	−	0.288112i	$-0.906973\pi$
$173$	−25.1904	−1.91519	−0.957597	+	0.288112i	$0.906973\pi$
$174$	0.0527245	0.00399703
$175$	4.54553	0.343610
$176$	−6.48034	−0.488474
$177$	−0.112623	−0.00846528
$178$	2.05416	0.153966
$179$	−5.99117	−0.447801	−0.223901	−	0.974612i	$-0.571879\pi$
$179$	−5.99117	−0.447801	−0.223901	+	0.974612i	$0.571879\pi$
$180$	9.26844	0.690828
$181$	0.795385	0.0591205	0.0295603	−	0.999563i	$-0.490589\pi$
$181$	0.795385	0.0591205	0.0295603	+	0.999563i	$0.490589\pi$
$182$	1.04019	0.0771041
$183$	−0.0858610	−0.00634703
$184$	8.22045	0.606020
$185$	11.6932	0.859704
$186$	0.0830477	0.00608935
$187$	−16.2926	−1.19143
$188$	−2.96047	−0.215915
$189$	−0.0606024	−0.00440817
$190$	0	0
$191$	−8.32524	−0.602393	−0.301197	−	0.953562i	$-0.597386\pi$
$191$	−8.32524	−0.602393	−0.301197	+	0.953562i	$0.597386\pi$
$192$	0.0101006	0.000728946 0
$193$	10.8225	0.779019	0.389510	−	0.921022i	$-0.372644\pi$
$193$	10.8225	0.779019	0.389510	+	0.921022i	$0.372644\pi$
$194$	−18.9122	−1.35782
$195$	0.0324608	0.00232456
$196$	1.00000	0.0714286
$197$	13.4869	0.960900	0.480450	−	0.877022i	$-0.340473\pi$
$197$	13.4869	0.960900	0.480450	+	0.877022i	$0.340473\pi$
$198$	−19.4404	−1.38157
$199$	1.65494	0.117316	0.0586579	−	0.998278i	$-0.481318\pi$
$199$	1.65494	0.117316	0.0586579	+	0.998278i	$0.481318\pi$
$200$	−4.54553	−0.321417
$201$	−0.125268	−0.00883571
$202$	6.26894	0.441081
$203$	−5.21995	−0.366369
$204$	0.0253944	0.00177796
$205$	−19.6463	−1.37215
$206$	9.62321	0.670481
$207$	24.6605	1.71402
$208$	−1.04019	−0.0721243
$209$	0	0
$210$	0.0312065	0.00215346
$211$	−5.54673	−0.381853	−0.190926	−	0.981604i	$-0.561149\pi$
$211$	−5.54673	−0.381853	−0.190926	+	0.981604i	$0.561149\pi$
$212$	0.538413	0.0369784
$213$	−0.0423232	−0.00289994
$214$	−3.50365	−0.239504
$215$	−4.11325	−0.280522
$216$	0.0606024	0.00412347
$217$	−8.22208	−0.558151
$218$	6.32193	0.428175
$219$	0.108040	0.00730069
$220$	20.0216	1.34985
$221$	−2.61520	−0.175917
$222$	0.0382279	0.00256569
$223$	11.0281	0.738498	0.369249	−	0.929331i	$-0.379615\pi$
$223$	11.0281	0.738498	0.369249	+	0.929331i	$0.379615\pi$
$224$	−1.00000	−0.0668153
$225$	−13.6361	−0.909075
$226$	9.17404	0.610248
$227$	−17.2648	−1.14591	−0.572953	−	0.819588i	$-0.694202\pi$
$227$	−17.2648	−1.14591	−0.572953	+	0.819588i	$0.694202\pi$
$228$	0	0
$229$	−12.7174	−0.840388	−0.420194	−	0.907434i	$-0.638038\pi$
$229$	−12.7174	−0.840388	−0.420194	+	0.907434i	$0.638038\pi$
$230$	−25.3978	−1.67468
$231$	−0.0654551	−0.00430663
$232$	5.21995	0.342707
$233$	11.7719	0.771202	0.385601	−	0.922666i	$-0.373994\pi$
$233$	11.7719	0.771202	0.385601	+	0.922666i	$0.373994\pi$
$234$	−3.12047	−0.203991
$235$	9.14663	0.596660
$236$	−11.1502	−0.725816
$237$	−0.108295	−0.00703453
$238$	−2.51415	−0.162968
$239$	−4.72614	−0.305708	−0.152854	−	0.988249i	$-0.548846\pi$
$239$	−4.72614	−0.305708	−0.152854	+	0.988249i	$0.548846\pi$
$240$	−0.0312065	−0.00201437
$241$	13.9003	0.895394	0.447697	−	0.894185i	$-0.352244\pi$
$241$	13.9003	0.895394	0.447697	+	0.894185i	$0.352244\pi$
$242$	−30.9948	−1.99242
$243$	0.272703	0.0174939
$244$	−8.50062	−0.544196
$245$	−3.08958	−0.197386
$246$	−0.0642282	−0.00409504
$247$	0	0
$248$	8.22208	0.522103
$249$	−0.0678945	−0.00430264
$250$	−1.40413	−0.0888050
$251$	−25.2161	−1.59163	−0.795813	−	0.605543i	$-0.792956\pi$
$251$	−25.2161	−1.59163	−0.795813	+	0.605543i	$0.792956\pi$
$252$	−2.99990	−0.188976
$253$	53.2713	3.34914
$254$	−15.2907	−0.959425
$255$	−0.0784580	−0.00491323
$256$	1.00000	0.0625000
$257$	9.55980	0.596324	0.298162	−	0.954515i	$-0.403626\pi$
$257$	9.55980	0.596324	0.298162	+	0.954515i	$0.403626\pi$
$258$	−0.0134472	−0.000837185 0
$259$	−3.78473	−0.235172
$260$	3.21376	0.199309
$261$	15.6593	0.969288
$262$	−11.9591	−0.738836
$263$	−20.9100	−1.28937	−0.644683	−	0.764450i	$-0.723011\pi$
$263$	−20.9100	−1.28937	−0.644683	+	0.764450i	$0.723011\pi$
$264$	0.0654551	0.00402848
$265$	−1.66347	−0.102186
$266$	0	0
$267$	−0.0207482	−0.00126977
$268$	−12.4021	−0.757576
$269$	11.5928	0.706823	0.353412	−	0.935468i	$-0.385022\pi$
$269$	11.5928	0.706823	0.353412	+	0.935468i	$0.385022\pi$
$270$	−0.187236	−0.0113948
$271$	7.17097	0.435605	0.217803	−	0.975993i	$-0.430111\pi$
$271$	7.17097	0.435605	0.217803	+	0.975993i	$0.430111\pi$
$272$	2.51415	0.152443
$273$	−0.0105065	−0.000635883 0
$274$	2.02231	0.122172
$275$	−29.4566	−1.77630
$276$	−0.0830312	−0.00499789
$277$	13.9958	0.840926	0.420463	−	0.907310i	$-0.361868\pi$
$277$	13.9958	0.840926	0.420463	+	0.907310i	$0.361868\pi$
$278$	−3.30573	−0.198264
$279$	24.6654	1.47668
$280$	3.08958	0.184638
$281$	−29.7098	−1.77234	−0.886169	−	0.463363i	$-0.846643\pi$
$281$	−29.7098	−1.77234	−0.886169	+	0.463363i	$0.846643\pi$
$282$	0.0299024	0.00178066
$283$	2.13918	0.127161	0.0635805	−	0.997977i	$-0.479748\pi$
$283$	2.13918	0.127161	0.0635805	+	0.997977i	$0.479748\pi$
$284$	−4.19018	−0.248641
$285$	0	0
$286$	−6.74079	−0.398592
$287$	6.35887	0.375352
$288$	2.99990	0.176771
$289$	−10.6790	−0.628179
$290$	−16.1275	−0.947038
$291$	0.191024	0.0111980
$292$	10.6965	0.625964
$293$	−5.59802	−0.327040	−0.163520	−	0.986540i	$-0.552285\pi$
$293$	−5.59802	−0.327040	−0.163520	+	0.986540i	$0.552285\pi$
$294$	−0.0101006	−0.000589077 0
$295$	34.4494	2.00572
$296$	3.78473	0.219983
$297$	0.392724	0.0227882
$298$	2.78517	0.161341
$299$	8.55084	0.494508
$300$	0.0459124	0.00265075
$301$	1.33133	0.0767366
$302$	13.5357	0.778891
$303$	−0.0633199	−0.00363763
$304$	0	0
$305$	26.2634	1.50384
$306$	7.54220	0.431159
$307$	8.43615	0.481477	0.240738	−	0.970590i	$-0.422610\pi$
$307$	8.43615	0.481477	0.240738	+	0.970590i	$0.422610\pi$
$308$	−6.48034	−0.369252
$309$	−0.0971999	−0.00552951
$310$	−25.4028	−1.44278
$311$	28.6974	1.62728	0.813639	−	0.581370i	$-0.197483\pi$
$311$	28.6974	1.62728	0.813639	+	0.581370i	$0.197483\pi$
$312$	0.0105065	0.000594815 0
$313$	2.82611	0.159741	0.0798707	−	0.996805i	$-0.474549\pi$
$313$	2.82611	0.159741	0.0798707	+	0.996805i	$0.474549\pi$
$314$	−3.10988	−0.175501
$315$	9.26844	0.522217
$316$	−10.7217	−0.603143
$317$	−20.3757	−1.14441	−0.572206	−	0.820110i	$-0.693912\pi$
$317$	−20.3757	−1.14441	−0.572206	+	0.820110i	$0.693912\pi$
$318$	−0.00543828	−0.000304964 0
$319$	33.8271	1.89395
$320$	−3.08958	−0.172713
$321$	0.0353888	0.00197521
$322$	8.22045	0.458108
$323$	0	0
$324$	8.99908	0.499949
$325$	−4.72822	−0.262274
$326$	−17.4728	−0.967731
$327$	−0.0638551	−0.00353119
$328$	−6.35887	−0.351110
$329$	−2.96047	−0.163216
$330$	−0.202229	−0.0111323
$331$	−4.28913	−0.235752	−0.117876	−	0.993028i	$-0.537609\pi$
$331$	−4.28913	−0.235752	−0.117876	+	0.993028i	$0.537609\pi$
$332$	−6.72185	−0.368910
$333$	11.3538	0.622185
$334$	−19.3247	−1.05740
$335$	38.3172	2.09349
$336$	0.0101006	0.000551031 0
$337$	−25.1195	−1.36835	−0.684173	−	0.729320i	$-0.739837\pi$
$337$	−25.1195	−1.36835	−0.684173	+	0.729320i	$0.739837\pi$
$338$	11.9180	0.648254
$339$	−0.0926630	−0.00503276
$340$	−7.76769	−0.421262
$341$	53.2819	2.88538
$342$	0	0
$343$	1.00000	0.0539949
$344$	−1.33133	−0.0717805
$345$	0.256532	0.0138112
$346$	25.1904	1.35425
$347$	4.61085	0.247523	0.123762	−	0.992312i	$-0.460504\pi$
$347$	4.61085	0.247523	0.123762	+	0.992312i	$0.460504\pi$
$348$	−0.0527245	−0.00282633
$349$	−10.8714	−0.581932	−0.290966	−	0.956733i	$-0.593977\pi$
$349$	−10.8714	−0.581932	−0.290966	+	0.956733i	$0.593977\pi$
$350$	−4.54553	−0.242969
$351$	0.0630380	0.00336472
$352$	6.48034	0.345403
$353$	17.6519	0.939517	0.469759	−	0.882795i	$-0.344341\pi$
$353$	17.6519	0.939517	0.469759	+	0.882795i	$0.344341\pi$
$354$	0.112623	0.00598586
$355$	12.9459	0.687097
$356$	−2.05416	−0.108871
$357$	0.0253944	0.00134401
$358$	5.99117	0.316643
$359$	−3.43963	−0.181537	−0.0907683	−	0.995872i	$-0.528932\pi$
$359$	−3.43963	−0.181537	−0.0907683	+	0.995872i	$0.528932\pi$
$360$	−9.26844	−0.488489
$361$	0	0
$362$	−0.795385	−0.0418045
$363$	0.313065	0.0164317
$364$	−1.04019	−0.0545208
$365$	−33.0476	−1.72979
$366$	0.0858610	0.00448803
$367$	−0.914050	−0.0477130	−0.0238565	−	0.999715i	$-0.507594\pi$
$367$	−0.914050	−0.0477130	−0.0238565	+	0.999715i	$0.507594\pi$
$368$	−8.22045	−0.428521
$369$	−19.0760	−0.993055
$370$	−11.6932	−0.607903
$371$	0.538413	0.0279530
$372$	−0.0830477	−0.00430582
$373$	21.4131	1.10873	0.554363	−	0.832275i	$-0.312962\pi$
$373$	21.4131	1.10873	0.554363	+	0.832275i	$0.312962\pi$
$374$	16.2926	0.842469
$375$	0.0141825	0.000732381 0
$376$	2.96047	0.152675
$377$	5.42975	0.279646
$378$	0.0606024	0.00311705
$379$	2.27615	0.116918	0.0584591	−	0.998290i	$-0.481381\pi$
$379$	2.27615	0.116918	0.0584591	+	0.998290i	$0.481381\pi$
$380$	0	0
$381$	0.154445	0.00791245
$382$	8.32524	0.425956
$383$	−3.73363	−0.190779	−0.0953897	−	0.995440i	$-0.530410\pi$
$383$	−3.73363	−0.190779	−0.0953897	+	0.995440i	$0.530410\pi$
$384$	−0.0101006	−0.000515442 0
$385$	20.0216	1.02039
$386$	−10.8225	−0.550850
$387$	−3.99385	−0.203019
$388$	18.9122	0.960122
$389$	4.92065	0.249487	0.124744	−	0.992189i	$-0.460189\pi$
$389$	4.92065	0.249487	0.124744	+	0.992189i	$0.460189\pi$
$390$	−0.0324608	−0.00164372
$391$	−20.6675	−1.04520
$392$	−1.00000	−0.0505076
$393$	0.120794	0.00609324
$394$	−13.4869	−0.679459
$395$	33.1256	1.66673
$396$	19.4404	0.976915
$397$	−13.6462	−0.684883	−0.342441	−	0.939539i	$-0.611254\pi$
$397$	−13.6462	−0.684883	−0.342441	+	0.939539i	$0.611254\pi$
$398$	−1.65494	−0.0829548
$399$	0	0
$400$	4.54553	0.227276
$401$	13.4469	0.671504	0.335752	−	0.941950i	$-0.391010\pi$
$401$	13.4469	0.671504	0.335752	+	0.941950i	$0.391010\pi$
$402$	0.125268	0.00624779
$403$	8.55254	0.426032
$404$	−6.26894	−0.311892
$405$	−27.8034	−1.38156
$406$	5.21995	0.259062
$407$	24.5263	1.21573
$408$	−0.0253944	−0.00125721
$409$	−33.3733	−1.65020	−0.825101	−	0.564986i	$-0.808882\pi$
$409$	−33.3733	−1.65020	−0.825101	+	0.564986i	$0.808882\pi$
$410$	19.6463	0.970260
$411$	−0.0204265	−0.00100756
$412$	−9.62321	−0.474102
$413$	−11.1502	−0.548665
$414$	−24.6605	−1.21200
$415$	20.7677	1.01945
$416$	1.04019	0.0509996
$417$	0.0333897	0.00163510
$418$	0	0
$419$	19.7549	0.965091	0.482545	−	0.875871i	$-0.339712\pi$
$419$	19.7549	0.965091	0.482545	+	0.875871i	$0.339712\pi$
$420$	−0.0312065	−0.00152272
$421$	33.0308	1.60982	0.804912	−	0.593395i	$-0.202213\pi$
$421$	33.0308	1.60982	0.804912	+	0.593395i	$0.202213\pi$
$422$	5.54673	0.270011
$423$	8.88111	0.431815
$424$	−0.538413	−0.0261477
$425$	11.4282	0.554347
$426$	0.0423232	0.00205056
$427$	−8.50062	−0.411374
$428$	3.50365	0.169355
$429$	0.0680858	0.00328721
$430$	4.11325	0.198359
$431$	−2.12221	−0.102223	−0.0511117	−	0.998693i	$-0.516276\pi$
$431$	−2.12221	−0.102223	−0.0511117	+	0.998693i	$0.516276\pi$
$432$	−0.0606024	−0.00291573
$433$	10.7964	0.518841	0.259421	−	0.965764i	$-0.416468\pi$
$433$	10.7964	0.518841	0.259421	+	0.965764i	$0.416468\pi$
$434$	8.22208	0.394673
$435$	0.162897	0.00781030
$436$	−6.32193	−0.302766
$437$	0	0
$438$	−0.108040	−0.00516237
$439$	−26.2118	−1.25102	−0.625510	−	0.780216i	$-0.715109\pi$
$439$	−26.2118	−1.25102	−0.625510	+	0.780216i	$0.715109\pi$
$440$	−20.0216	−0.954490
$441$	−2.99990	−0.142852
$442$	2.61520	0.124392
$443$	17.9877	0.854624	0.427312	−	0.904104i	$-0.359461\pi$
$443$	17.9877	0.854624	0.427312	+	0.904104i	$0.359461\pi$
$444$	−0.0382279	−0.00181422
$445$	6.34651	0.300854
$446$	−11.0281	−0.522197
$447$	−0.0281318	−0.00133059
$448$	1.00000	0.0472456
$449$	−32.7512	−1.54563	−0.772813	−	0.634633i	$-0.781151\pi$
$449$	−32.7512	−1.54563	−0.772813	+	0.634633i	$0.781151\pi$
$450$	13.6361	0.642813
$451$	−41.2077	−1.94039
$452$	−9.17404	−0.431511
$453$	−0.136718	−0.00642357
$454$	17.2648	0.810278
$455$	3.21376	0.150663
$456$	0	0
$457$	−5.38681	−0.251984	−0.125992	−	0.992031i	$-0.540211\pi$
$457$	−5.38681	−0.251984	−0.125992	+	0.992031i	$0.540211\pi$
$458$	12.7174	0.594244
$459$	−0.152364	−0.00711172
$460$	25.3978	1.18418
$461$	1.59769	0.0744120	0.0372060	−	0.999308i	$-0.488154\pi$
$461$	1.59769	0.0744120	0.0372060	+	0.999308i	$0.488154\pi$
$462$	0.0654551	0.00304525
$463$	22.7541	1.05747	0.528736	−	0.848786i	$-0.322666\pi$
$463$	22.7541	1.05747	0.528736	+	0.848786i	$0.322666\pi$
$464$	−5.21995	−0.242330
$465$	0.256583	0.0118987
$466$	−11.7719	−0.545322
$467$	−9.02572	−0.417660	−0.208830	−	0.977952i	$-0.566966\pi$
$467$	−9.02572	−0.417660	−0.208830	+	0.977952i	$0.566966\pi$
$468$	3.12047	0.144244
$469$	−12.4021	−0.572674
$470$	−9.14663	−0.421902
$471$	0.0314116	0.00144737
$472$	11.1502	0.513229
$473$	−8.62747	−0.396691
$474$	0.108295	0.00497417
$475$	0	0
$476$	2.51415	0.115236
$477$	−1.61519	−0.0739543
$478$	4.72614	0.216168
$479$	−22.8473	−1.04392	−0.521959	−	0.852971i	$-0.674799\pi$
$479$	−22.8473	−1.04392	−0.521959	+	0.852971i	$0.674799\pi$
$480$	0.0312065	0.00142438
$481$	3.93684	0.179505
$482$	−13.9003	−0.633139
$483$	−0.0830312	−0.00377805
$484$	30.9948	1.40886
$485$	−58.4309	−2.65321
$486$	−0.272703	−0.0123701
$487$	−3.43266	−0.155549	−0.0777743	−	0.996971i	$-0.524781\pi$
$487$	−3.43266	−0.155549	−0.0777743	+	0.996971i	$0.524781\pi$
$488$	8.50062	0.384805
$489$	0.176486	0.00798095
$490$	3.08958	0.139573
$491$	32.6228	1.47225	0.736124	−	0.676847i	$-0.236654\pi$
$491$	32.6228	1.47225	0.736124	+	0.676847i	$0.236654\pi$
$492$	0.0642282	0.00289563
$493$	−13.1238	−0.591064
$494$	0	0
$495$	−60.0626	−2.69961
$496$	−8.22208	−0.369182
$497$	−4.19018	−0.187955
$498$	0.0678945	0.00304243
$499$	−6.74925	−0.302138	−0.151069	−	0.988523i	$-0.548272\pi$
$499$	−6.74925	−0.302138	−0.151069	+	0.988523i	$0.548272\pi$
$500$	1.40413	0.0627946
$501$	0.195190	0.00872045
$502$	25.2161	1.12545
$503$	3.23730	0.144344	0.0721719	−	0.997392i	$-0.477007\pi$
$503$	3.23730	0.144344	0.0721719	+	0.997392i	$0.477007\pi$
$504$	2.99990	0.133626
$505$	19.3684	0.861884
$506$	−53.2713	−2.36820
$507$	−0.120379	−0.00534620
$508$	15.2907	0.678416
$509$	−7.66874	−0.339911	−0.169955	−	0.985452i	$-0.554362\pi$
$509$	−7.66874	−0.339911	−0.169955	+	0.985452i	$0.554362\pi$
$510$	0.0784580	0.00347418
$511$	10.6965	0.473184
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−9.55980	−0.421665
$515$	29.7317	1.31014
$516$	0.0134472	0.000591979 0
$517$	19.1849	0.843750
$518$	3.78473	0.166291
$519$	−0.254438	−0.0111686
$520$	−3.21376	−0.140933
$521$	26.6530	1.16769	0.583844	−	0.811866i	$-0.301548\pi$
$521$	26.6530	1.16769	0.583844	+	0.811866i	$0.301548\pi$
$522$	−15.6593	−0.685390
$523$	−11.0944	−0.485124	−0.242562	−	0.970136i	$-0.577988\pi$
$523$	−11.0944	−0.485124	−0.242562	+	0.970136i	$0.577988\pi$
$524$	11.9591	0.522436
$525$	0.0459124	0.00200378
$526$	20.9100	0.911719
$527$	−20.6716	−0.900468
$528$	−0.0654551	−0.00284857
$529$	44.5759	1.93808
$530$	1.66347	0.0722567
$531$	33.4494	1.45158
$532$	0	0
$533$	−6.61444	−0.286503
$534$	0.0207482	0.000897864 0
$535$	−10.8248	−0.467997
$536$	12.4021	0.535687
$537$	−0.0605142	−0.00261138
$538$	−11.5928	−0.499800
$539$	−6.48034	−0.279128
$540$	0.187236	0.00805736
$541$	6.05567	0.260354	0.130177	−	0.991491i	$-0.458446\pi$
$541$	6.05567	0.260354	0.130177	+	0.991491i	$0.458446\pi$
$542$	−7.17097	−0.308019
$543$	0.00803384	0.000344765 0
$544$	−2.51415	−0.107793
$545$	19.5321	0.836665
$546$	0.0105065	0.000449638 0
$547$	−8.32747	−0.356057	−0.178028	−	0.984025i	$-0.556972\pi$
$547$	−8.32747	−0.356057	−0.178028	+	0.984025i	$0.556972\pi$
$548$	−2.02231	−0.0863889
$549$	25.5010	1.08836
$550$	29.4566	1.25603
$551$	0	0
$552$	0.0830312	0.00353404
$553$	−10.7217	−0.455933
$554$	−13.9958	−0.594625
$555$	0.118108	0.00501342
$556$	3.30573	0.140194
$557$	−4.33985	−0.183885	−0.0919426	−	0.995764i	$-0.529308\pi$
$557$	−4.33985	−0.183885	−0.0919426	+	0.995764i	$0.529308\pi$
$558$	−24.6654	−1.04417
$559$	−1.38484	−0.0585724
$560$	−3.08958	−0.130559
$561$	−0.164564	−0.00694790
$562$	29.7098	1.25323
$563$	26.9610	1.13627	0.568135	−	0.822936i	$-0.307665\pi$
$563$	26.9610	1.13627	0.568135	+	0.822936i	$0.307665\pi$
$564$	−0.0299024	−0.00125912
$565$	28.3440	1.19244
$566$	−2.13918	−0.0899165
$567$	8.99908	0.377926
$568$	4.19018	0.175816
$569$	36.7221	1.53947	0.769735	−	0.638363i	$-0.220388\pi$
$569$	36.7221	1.53947	0.769735	+	0.638363i	$0.220388\pi$
$570$	0	0
$571$	29.8979	1.25119	0.625594	−	0.780148i	$-0.284857\pi$
$571$	29.8979	1.25119	0.625594	+	0.780148i	$0.284857\pi$
$572$	6.74079	0.281847
$573$	−0.0840896	−0.00351290
$574$	−6.35887	−0.265414
$575$	−37.3663	−1.55828
$576$	−2.99990	−0.124996
$577$	−44.4133	−1.84895	−0.924475	−	0.381244i	$-0.875496\pi$
$577$	−44.4133	−1.84895	−0.924475	+	0.381244i	$0.875496\pi$
$578$	10.6790	0.444189
$579$	0.109313	0.00454290
$580$	16.1275	0.669657
$581$	−6.72185	−0.278870
$582$	−0.191024	−0.00791820
$583$	−3.48910	−0.144504
$584$	−10.6965	−0.442623
$585$	−9.64095	−0.398604
$586$	5.59802	0.231252
$587$	33.6128	1.38735	0.693675	−	0.720288i	$-0.255990\pi$
$587$	33.6128	1.38735	0.693675	+	0.720288i	$0.255990\pi$
$588$	0.0101006	0.000416540 0
$589$	0	0
$590$	−34.4494	−1.41826
$591$	0.136225	0.00560355
$592$	−3.78473	−0.155551
$593$	−28.8352	−1.18412	−0.592060	−	0.805894i	$-0.701685\pi$
$593$	−28.8352	−1.18412	−0.592060	+	0.805894i	$0.701685\pi$
$594$	−0.392724	−0.0161137
$595$	−7.76769	−0.318444
$596$	−2.78517	−0.114085
$597$	0.0167159	0.000684135 0
$598$	−8.55084	−0.349670
$599$	31.6279	1.29228	0.646141	−	0.763218i	$-0.276382\pi$
$599$	31.6279	1.29228	0.646141	+	0.763218i	$0.276382\pi$
$600$	−0.0459124	−0.00187437
$601$	8.00902	0.326695	0.163347	−	0.986569i	$-0.447771\pi$
$601$	8.00902	0.326695	0.163347	+	0.986569i	$0.447771\pi$
$602$	−1.33133	−0.0542609
$603$	37.2049	1.51510
$604$	−13.5357	−0.550759
$605$	−95.7611	−3.89324
$606$	0.0633199	0.00257219
$607$	−25.3888	−1.03050	−0.515250	−	0.857040i	$-0.672301\pi$
$607$	−25.3888	−1.03050	−0.515250	+	0.857040i	$0.672301\pi$
$608$	0	0
$609$	−0.0527245	−0.00213650
$610$	−26.2634	−1.06337
$611$	3.07946	0.124581
$612$	−7.54220	−0.304875
$613$	37.8223	1.52763	0.763813	−	0.645437i	$-0.223325\pi$
$613$	37.8223	1.52763	0.763813	+	0.645437i	$0.223325\pi$
$614$	−8.43615	−0.340455
$615$	−0.198438	−0.00800181
$616$	6.48034	0.261100
$617$	9.21098	0.370820	0.185410	−	0.982661i	$-0.440639\pi$
$617$	9.21098	0.370820	0.185410	+	0.982661i	$0.440639\pi$
$618$	0.0971999	0.00390995
$619$	−32.8101	−1.31875	−0.659375	−	0.751814i	$-0.729179\pi$
$619$	−32.8101	−1.31875	−0.659375	+	0.751814i	$0.729179\pi$
$620$	25.4028	1.02020
$621$	0.498179	0.0199912
$622$	−28.6974	−1.15066
$623$	−2.05416	−0.0822984
$624$	−0.0105065	−0.000420597 0
$625$	−27.0658	−1.08263
$626$	−2.82611	−0.112954
$627$	0	0
$628$	3.10988	0.124098
$629$	−9.51539	−0.379403
$630$	−9.26844	−0.369263
$631$	24.1564	0.961652	0.480826	−	0.876816i	$-0.340337\pi$
$631$	24.1564	0.961652	0.480826	+	0.876816i	$0.340337\pi$
$632$	10.7217	0.426487
$633$	−0.0560251	−0.00222680
$634$	20.3757	0.809222
$635$	−47.2420	−1.87474
$636$	0.00543828	0.000215642 0
$637$	−1.04019	−0.0412139
$638$	−33.8271	−1.33923
$639$	12.5701	0.497266
$640$	3.08958	0.122127
$641$	−14.2534	−0.562974	−0.281487	−	0.959565i	$-0.590828\pi$
$641$	−14.2534	−0.562974	−0.281487	+	0.959565i	$0.590828\pi$
$642$	−0.0353888	−0.00139669
$643$	−12.3782	−0.488150	−0.244075	−	0.969756i	$-0.578484\pi$
$643$	−12.3782	−0.488150	−0.244075	+	0.969756i	$0.578484\pi$
$644$	−8.22045	−0.323931
$645$	−0.0415462	−0.00163588
$646$	0	0
$647$	−29.9832	−1.17876	−0.589380	−	0.807856i	$-0.700628\pi$
$647$	−29.9832	−1.17876	−0.589380	+	0.807856i	$0.700628\pi$
$648$	−8.99908	−0.353517
$649$	72.2570	2.83634
$650$	4.72822	0.185456
$651$	−0.0830477	−0.00325490
$652$	17.4728	0.684289
$653$	14.8776	0.582205	0.291103	−	0.956692i	$-0.405978\pi$
$653$	14.8776	0.582205	0.291103	+	0.956692i	$0.405978\pi$
$654$	0.0638551	0.00249693
$655$	−36.9487	−1.44370
$656$	6.35887	0.248272
$657$	−32.0883	−1.25188
$658$	2.96047	0.115411
$659$	−8.91326	−0.347211	−0.173606	−	0.984815i	$-0.555542\pi$
$659$	−8.91326	−0.347211	−0.173606	+	0.984815i	$0.555542\pi$
$660$	0.202229	0.00787176
$661$	32.0483	1.24653	0.623267	−	0.782009i	$-0.285805\pi$
$661$	32.0483	1.24653	0.623267	+	0.782009i	$0.285805\pi$
$662$	4.28913	0.166702
$663$	−0.0264150	−0.00102587
$664$	6.72185	0.260859
$665$	0	0
$666$	−11.3538	−0.439951
$667$	42.9104	1.66150
$668$	19.3247	0.747694
$669$	0.111390	0.00430660
$670$	−38.3172	−1.48032
$671$	55.0869	2.12661
$672$	−0.0101006	−0.000389638 0
$673$	−26.0783	−1.00525	−0.502623	−	0.864506i	$-0.667632\pi$
$673$	−26.0783	−1.00525	−0.502623	+	0.864506i	$0.667632\pi$
$674$	25.1195	0.967567
$675$	−0.275470	−0.0106028
$676$	−11.9180	−0.458385
$677$	−35.1829	−1.35219	−0.676094	−	0.736816i	$-0.736329\pi$
$677$	−35.1829	−1.35219	−0.676094	+	0.736816i	$0.736329\pi$
$678$	0.0926630	0.00355870
$679$	18.9122	0.725784
$680$	7.76769	0.297877
$681$	−0.174384	−0.00668242
$682$	−53.2819	−2.04027
$683$	−3.59264	−0.137468	−0.0687342	−	0.997635i	$-0.521896\pi$
$683$	−3.59264	−0.137468	−0.0687342	+	0.997635i	$0.521896\pi$
$684$	0	0
$685$	6.24810	0.238728
$686$	−1.00000	−0.0381802
$687$	−0.128453	−0.00490077
$688$	1.33133	0.0507565
$689$	−0.560053	−0.0213363
$690$	−0.256532	−0.00976600
$691$	−48.5708	−1.84772	−0.923860	−	0.382731i	$-0.874984\pi$
$691$	−48.5708	−1.84772	−0.923860	+	0.382731i	$0.874984\pi$
$692$	−25.1904	−0.957597
$693$	19.4404	0.738478
$694$	−4.61085	−0.175025
$695$	−10.2133	−0.387413
$696$	0.0527245	0.00199852
$697$	15.9872	0.605557
$698$	10.8714	0.411488
$699$	0.118903	0.00449731
$700$	4.54553	0.171805
$701$	−7.27771	−0.274875	−0.137438	−	0.990510i	$-0.543887\pi$
$701$	−7.27771	−0.274875	−0.137438	+	0.990510i	$0.543887\pi$
$702$	−0.0630380	−0.00237922
$703$	0	0
$704$	−6.48034	−0.244237
$705$	0.0923861	0.00347946
$706$	−17.6519	−0.664339
$707$	−6.26894	−0.235768
$708$	−0.112623	−0.00423264
$709$	−12.7707	−0.479612	−0.239806	−	0.970821i	$-0.577084\pi$
$709$	−12.7707	−0.479612	−0.239806	+	0.970821i	$0.577084\pi$
$710$	−12.9459	−0.485851
$711$	32.1640	1.20625
$712$	2.05416	0.0769831
$713$	67.5892	2.53124
$714$	−0.0253944	−0.000950360 0
$715$	−20.8262	−0.778858
$716$	−5.99117	−0.223901
$717$	−0.0477366	−0.00178276
$718$	3.43963	0.128366
$719$	7.50585	0.279921	0.139960	−	0.990157i	$-0.455302\pi$
$719$	7.50585	0.279921	0.139960	+	0.990157i	$0.455302\pi$
$720$	9.26844	0.345414
$721$	−9.62321	−0.358387
$722$	0	0
$723$	0.140400	0.00522155
$724$	0.795385	0.0295603
$725$	−23.7274	−0.881215
$726$	−0.313065	−0.0116189
$727$	−31.5011	−1.16831	−0.584156	−	0.811641i	$-0.698575\pi$
$727$	−31.5011	−1.16831	−0.584156	+	0.811641i	$0.698575\pi$
$728$	1.04019	0.0385521
$729$	−26.9945	−0.999796
$730$	33.0476	1.22315
$731$	3.34717	0.123799
$732$	−0.0858610	−0.00317352
$733$	−0.0818415	−0.00302288	−0.00151144	−	0.999999i	$-0.500481\pi$
$733$	−0.0818415	−0.00302288	−0.00151144	+	0.999999i	$0.500481\pi$
$734$	0.914050	0.0337382
$735$	−0.0312065	−0.00115107
$736$	8.22045	0.303010
$737$	80.3696	2.96045
$738$	19.0760	0.702196
$739$	15.9745	0.587630	0.293815	−	0.955862i	$-0.405075\pi$
$739$	15.9745	0.587630	0.293815	+	0.955862i	$0.405075\pi$
$740$	11.6932	0.429852
$741$	0	0
$742$	−0.538413	−0.0197658
$743$	−38.2830	−1.40447	−0.702233	−	0.711947i	$-0.747814\pi$
$743$	−38.2830	−1.40447	−0.702233	+	0.711947i	$0.747814\pi$
$744$	0.0830477	0.00304468
$745$	8.60502	0.315264
$746$	−21.4131	−0.783988
$747$	20.1649	0.737794
$748$	−16.2926	−0.595715
$749$	3.50365	0.128020
$750$	−0.0141825	−0.000517872 0
$751$	−12.4262	−0.453437	−0.226719	−	0.973960i	$-0.572800\pi$
$751$	−12.4262	−0.453437	−0.226719	+	0.973960i	$0.572800\pi$
$752$	−2.96047	−0.107957
$753$	−0.254697	−0.00928166
$754$	−5.42975	−0.197740
$755$	41.8196	1.52197
$756$	−0.0606024	−0.00220409
$757$	32.4379	1.17898	0.589488	−	0.807777i	$-0.299330\pi$
$757$	32.4379	1.17898	0.589488	+	0.807777i	$0.299330\pi$
$758$	−2.27615	−0.0826736
$759$	0.538071	0.0195307
$760$	0	0
$761$	−46.4635	−1.68430	−0.842151	−	0.539242i	$-0.818711\pi$
$761$	−46.4635	−1.68430	−0.842151	+	0.539242i	$0.818711\pi$
$762$	−0.154445	−0.00559495
$763$	−6.32193	−0.228869
$764$	−8.32524	−0.301197
$765$	23.3023	0.842495
$766$	3.73363	0.134901
$767$	11.5983	0.418791
$768$	0.0101006	0.000364473 0
$769$	−12.6954	−0.457807	−0.228903	−	0.973449i	$-0.573514\pi$
$769$	−12.6954	−0.457807	−0.228903	+	0.973449i	$0.573514\pi$
$770$	−20.0216	−0.721527
$771$	0.0965594	0.00347750
$772$	10.8225	0.389510
$773$	−37.3592	−1.34372	−0.671859	−	0.740679i	$-0.734504\pi$
$773$	−37.3592	−1.34372	−0.671859	+	0.740679i	$0.734504\pi$
$774$	3.99385	0.143556
$775$	−37.3737	−1.34250
$776$	−18.9122	−0.678909
$777$	−0.0382279	−0.00137142
$778$	−4.92065	−0.176414
$779$	0	0
$780$	0.0324608	0.00116228
$781$	27.1538	0.971639
$782$	20.6675	0.739067
$783$	0.316342	0.0113051
$784$	1.00000	0.0357143
$785$	−9.60825	−0.342933
$786$	−0.120794	−0.00430857
$787$	−22.2346	−0.792579	−0.396290	−	0.918126i	$-0.629702\pi$
$787$	−22.2346	−0.792579	−0.396290	+	0.918126i	$0.629702\pi$
$788$	13.4869	0.480450
$789$	−0.211203	−0.00751902
$790$	−33.1256	−1.17856
$791$	−9.17404	−0.326191
$792$	−19.4404	−0.690783
$793$	8.84227	0.313998
$794$	13.6462	0.484285
$795$	−0.0168020	−0.000595906 0
$796$	1.65494	0.0586579
$797$	9.30447	0.329581	0.164791	−	0.986329i	$-0.447305\pi$
$797$	9.30447	0.329581	0.164791	+	0.986329i	$0.447305\pi$
$798$	0	0
$799$	−7.44308	−0.263317
$800$	−4.54553	−0.160709
$801$	6.16228	0.217734
$802$	−13.4469	−0.474825
$803$	−69.3168	−2.44614
$804$	−0.125268	−0.00441786
$805$	25.3978	0.895154
$806$	−8.55254	−0.301250
$807$	0.117093	0.00412189
$808$	6.26894	0.220541
$809$	29.7809	1.04704	0.523520	−	0.852013i	$-0.324619\pi$
$809$	29.7809	1.04704	0.523520	+	0.852013i	$0.324619\pi$
$810$	27.8034	0.976912
$811$	−24.6007	−0.863846	−0.431923	−	0.901910i	$-0.642165\pi$
$811$	−24.6007	−0.863846	−0.431923	+	0.901910i	$0.642165\pi$
$812$	−5.21995	−0.183184
$813$	0.0724308	0.00254026
$814$	−24.5263	−0.859648
$815$	−53.9838	−1.89097
$816$	0.0253944	0.000888980 0
$817$	0	0
$818$	33.3733	1.16687
$819$	3.12047	0.109038
$820$	−19.6463	−0.686077
$821$	−17.4772	−0.609957	−0.304979	−	0.952359i	$-0.598649\pi$
$821$	−17.4772	−0.609957	−0.304979	+	0.952359i	$0.598649\pi$
$822$	0.0204265	0.000712456 0
$823$	−3.12020	−0.108763	−0.0543816	−	0.998520i	$-0.517319\pi$
$823$	−3.12020	−0.108763	−0.0543816	+	0.998520i	$0.517319\pi$
$824$	9.62321	0.335241
$825$	−0.297528	−0.0103586
$826$	11.1502	0.387965
$827$	−29.0526	−1.01026	−0.505129	−	0.863044i	$-0.668555\pi$
$827$	−29.0526	−1.01026	−0.505129	+	0.863044i	$0.668555\pi$
$828$	24.6605	0.857012
$829$	−15.7312	−0.546369	−0.273184	−	0.961962i	$-0.588077\pi$
$829$	−15.7312	−0.546369	−0.273184	+	0.961962i	$0.588077\pi$
$830$	−20.7677	−0.720858
$831$	0.141365	0.00490391
$832$	−1.04019	−0.0360621
$833$	2.51415	0.0871102
$834$	−0.0333897	−0.00115619
$835$	−59.7052	−2.06618
$836$	0	0
$837$	0.498278	0.0172230
$838$	−19.7549	−0.682422
$839$	−56.0759	−1.93595	−0.967977	−	0.251038i	$-0.919228\pi$
$839$	−56.0759	−1.93595	−0.967977	+	0.251038i	$0.919228\pi$
$840$	0.0312065	0.00107673
$841$	−1.75209	−0.0604167
$842$	−33.0308	−1.13832
$843$	−0.300086	−0.0103355
$844$	−5.54673	−0.190926
$845$	36.8217	1.26670
$846$	−8.88111	−0.305339
$847$	30.9948	1.06499
$848$	0.538413	0.0184892
$849$	0.0216069	0.000741548 0
$850$	−11.4282	−0.391982
$851$	31.1122	1.06651
$852$	−0.0423232	−0.00144997
$853$	−37.1508	−1.27202	−0.636010	−	0.771681i	$-0.719416\pi$
$853$	−37.1508	−1.27202	−0.636010	+	0.771681i	$0.719416\pi$
$854$	8.50062	0.290885
$855$	0	0
$856$	−3.50365	−0.119752
$857$	32.6489	1.11527	0.557633	−	0.830088i	$-0.311710\pi$
$857$	32.6489	1.11527	0.557633	+	0.830088i	$0.311710\pi$
$858$	−0.0680858	−0.00232441
$859$	2.91728	0.0995365	0.0497682	−	0.998761i	$-0.484152\pi$
$859$	2.91728	0.0995365	0.0497682	+	0.998761i	$0.484152\pi$
$860$	−4.11325	−0.140261
$861$	0.0642282	0.00218889
$862$	2.12221	0.0722828
$863$	46.8384	1.59440	0.797199	−	0.603716i	$-0.206314\pi$
$863$	46.8384	1.59440	0.797199	+	0.603716i	$0.206314\pi$
$864$	0.0606024	0.00206173
$865$	77.8280	2.64623
$866$	−10.7964	−0.366876
$867$	−0.107864	−0.00366326
$868$	−8.22208	−0.279076
$869$	69.4803	2.35696
$870$	−0.162897	−0.00552272
$871$	12.9005	0.437117
$872$	6.32193	0.214088
$873$	−56.7347	−1.92018
$874$	0	0
$875$	1.40413	0.0474683
$876$	0.108040	0.00365035
$877$	−3.91938	−0.132348	−0.0661740	−	0.997808i	$-0.521079\pi$
$877$	−3.91938	−0.132348	−0.0661740	+	0.997808i	$0.521079\pi$
$878$	26.2118	0.884605
$879$	−0.0565432	−0.00190716
$880$	20.0216	0.674927
$881$	−10.9956	−0.370451	−0.185225	−	0.982696i	$-0.559302\pi$
$881$	−10.9956	−0.370451	−0.185225	+	0.982696i	$0.559302\pi$
$882$	2.99990	0.101012
$883$	12.5299	0.421664	0.210832	−	0.977522i	$-0.432383\pi$
$883$	12.5299	0.421664	0.210832	+	0.977522i	$0.432383\pi$
$884$	−2.61520	−0.0879587
$885$	0.347959	0.0116965
$886$	−17.9877	−0.604310
$887$	20.2854	0.681118	0.340559	−	0.940223i	$-0.389384\pi$
$887$	20.2854	0.681118	0.340559	+	0.940223i	$0.389384\pi$
$888$	0.0382279	0.00128284
$889$	15.2907	0.512834
$890$	−6.34651	−0.212736
$891$	−58.3171	−1.95370
$892$	11.0281	0.369249
$893$	0	0
$894$	0.0281318	0.000940869 0
$895$	18.5102	0.618729
$896$	−1.00000	−0.0334077
$897$	0.0863684	0.00288376
$898$	32.7512	1.09292
$899$	42.9189	1.43143
$900$	−13.6361	−0.454537
$901$	1.35365	0.0450967
$902$	41.2077	1.37206
$903$	0.0134472	0.000447494 0
$904$	9.17404	0.305124
$905$	−2.45741	−0.0816871
$906$	0.136718	0.00454215
$907$	11.5309	0.382877	0.191438	−	0.981505i	$-0.438685\pi$
$907$	11.5309	0.382877	0.191438	+	0.981505i	$0.438685\pi$
$908$	−17.2648	−0.572953
$909$	18.8062	0.623762
$910$	−3.21376	−0.106535
$911$	41.6454	1.37978	0.689888	−	0.723917i	$-0.257660\pi$
$911$	41.6454	1.37978	0.689888	+	0.723917i	$0.257660\pi$
$912$	0	0
$913$	43.5599	1.44162
$914$	5.38681	0.178180
$915$	0.265275	0.00876972
$916$	−12.7174	−0.420194
$917$	11.9591	0.394924
$918$	0.152364	0.00502875
$919$	4.43674	0.146354	0.0731772	−	0.997319i	$-0.476686\pi$
$919$	4.43674	0.146354	0.0731772	+	0.997319i	$0.476686\pi$
$920$	−25.3978	−0.837340
$921$	0.0852099	0.00280776
$922$	−1.59769	−0.0526172
$923$	4.35859	0.143465
$924$	−0.0654551	−0.00215332
$925$	−17.2036	−0.565651
$926$	−22.7541	−0.747746
$927$	28.8687	0.948171
$928$	5.21995	0.171353
$929$	4.66397	0.153020	0.0765099	−	0.997069i	$-0.475622\pi$
$929$	4.66397	0.153020	0.0765099	+	0.997069i	$0.475622\pi$
$930$	−0.256583	−0.00841368
$931$	0	0
$932$	11.7719	0.385601
$933$	0.289860	0.00948958
$934$	9.02572	0.295331
$935$	50.3373	1.64620
$936$	−3.12047	−0.101996
$937$	4.99598	0.163212	0.0816058	−	0.996665i	$-0.473995\pi$
$937$	4.99598	0.163212	0.0816058	+	0.996665i	$0.473995\pi$
$938$	12.4021	0.404942
$939$	0.0285453	0.000931542 0
$940$	9.14663	0.298330
$941$	−15.6005	−0.508561	−0.254280	−	0.967131i	$-0.581839\pi$
$941$	−15.6005	−0.508561	−0.254280	+	0.967131i	$0.581839\pi$
$942$	−0.0314116	−0.00102344
$943$	−52.2728	−1.70224
$944$	−11.1502	−0.362908
$945$	0.187236	0.00609079
$946$	8.62747	0.280503
$947$	46.7820	1.52021	0.760105	−	0.649800i	$-0.225148\pi$
$947$	46.7820	1.52021	0.760105	+	0.649800i	$0.225148\pi$
$948$	−0.108295	−0.00351727
$949$	−11.1264	−0.361177
$950$	0	0
$951$	−0.205806	−0.00667371
$952$	−2.51415	−0.0814842
$953$	−5.63281	−0.182465	−0.0912323	−	0.995830i	$-0.529081\pi$
$953$	−5.63281	−0.182465	−0.0912323	+	0.995830i	$0.529081\pi$
$954$	1.61519	0.0522936
$955$	25.7215	0.832329
$956$	−4.72614	−0.152854
$957$	0.341673	0.0110447
$958$	22.8473	0.738161
$959$	−2.02231	−0.0653039
$960$	−0.0312065	−0.00100719
$961$	36.6026	1.18073
$962$	−3.93684	−0.126929
$963$	−10.5106	−0.338699
$964$	13.9003	0.447697
$965$	−33.4370	−1.07637
$966$	0.0830312	0.00267149
$967$	−17.2008	−0.553142	−0.276571	−	0.960994i	$-0.589198\pi$
$967$	−17.2008	−0.553142	−0.276571	+	0.960994i	$0.589198\pi$
$968$	−30.9948	−0.996211
$969$	0	0
$970$	58.4309	1.87610
$971$	−13.8031	−0.442964	−0.221482	−	0.975164i	$-0.571089\pi$
$971$	−13.8031	−0.442964	−0.221482	+	0.975164i	$0.571089\pi$
$972$	0.272703	0.00874695
$973$	3.30573	0.105977
$974$	3.43266	0.109990
$975$	−0.0477577	−0.00152947
$976$	−8.50062	−0.272098
$977$	−28.4489	−0.910160	−0.455080	−	0.890451i	$-0.650389\pi$
$977$	−28.4489	−0.910160	−0.455080	+	0.890451i	$0.650389\pi$
$978$	−0.176486	−0.00564339
$979$	13.3117	0.425443
$980$	−3.08958	−0.0986931
$981$	18.9651	0.605511
$982$	−32.6228	−1.04104
$983$	−34.0184	−1.08502	−0.542509	−	0.840050i	$-0.682526\pi$
$983$	−34.0184	−1.08502	−0.542509	+	0.840050i	$0.682526\pi$
$984$	−0.0642282	−0.00204752
$985$	−41.6688	−1.32768
$986$	13.1238	0.417946
$987$	−0.0299024	−0.000951805 0
$988$	0	0
$989$	−10.9441	−0.348003
$990$	60.0626	1.90892
$991$	−15.0721	−0.478781	−0.239391	−	0.970923i	$-0.576948\pi$
$991$	−15.0721	−0.478781	−0.239391	+	0.970923i	$0.576948\pi$
$992$	8.22208	0.261051
$993$	−0.0433227	−0.00137480
$994$	4.19018	0.132904
$995$	−5.11309	−0.162096
$996$	−0.0678945	−0.00215132
$997$	24.1291	0.764176	0.382088	−	0.924126i	$-0.375205\pi$
$997$	24.1291	0.764176	0.382088	+	0.924126i	$0.375205\pi$
$998$	6.74925	0.213644
$999$	0.229364	0.00725674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bl.1.7		12
19.9	even	9		266.2.u.d.43.3	✓	24
19.17	even	9		266.2.u.d.99.3	yes	24
19.18	odd	2		5054.2.a.bm.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.43.3	✓	24	19.9	even	9
266.2.u.d.99.3	yes	24	19.17	even	9
5054.2.a.bl.1.7		12	1.1	even	1	trivial
5054.2.a.bm.1.6		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0101006 q^{3} +1.00000 q^{4} -3.08958 q^{5} -0.0101006 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99990 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0101006 q^{3} +1.00000 q^{4} -3.08958 q^{5} -0.0101006 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99990 q^{9} +3.08958 q^{10} -6.48034 q^{11} +0.0101006 q^{12} -1.04019 q^{13} -1.00000 q^{14} -0.0312065 q^{15} +1.00000 q^{16} +2.51415 q^{17} +2.99990 q^{18} -3.08958 q^{20} +0.0101006 q^{21} +6.48034 q^{22} -8.22045 q^{23} -0.0101006 q^{24} +4.54553 q^{25} +1.04019 q^{26} -0.0606024 q^{27} +1.00000 q^{28} -5.21995 q^{29} +0.0312065 q^{30} -8.22208 q^{31} -1.00000 q^{32} -0.0654551 q^{33} -2.51415 q^{34} -3.08958 q^{35} -2.99990 q^{36} -3.78473 q^{37} -0.0105065 q^{39} +3.08958 q^{40} +6.35887 q^{41} -0.0101006 q^{42} +1.33133 q^{43} -6.48034 q^{44} +9.26844 q^{45} +8.22045 q^{46} -2.96047 q^{47} +0.0101006 q^{48} +1.00000 q^{49} -4.54553 q^{50} +0.0253944 q^{51} -1.04019 q^{52} +0.538413 q^{53} +0.0606024 q^{54} +20.0216 q^{55} -1.00000 q^{56} +5.21995 q^{58} -11.1502 q^{59} -0.0312065 q^{60} -8.50062 q^{61} +8.22208 q^{62} -2.99990 q^{63} +1.00000 q^{64} +3.21376 q^{65} +0.0654551 q^{66} -12.4021 q^{67} +2.51415 q^{68} -0.0830312 q^{69} +3.08958 q^{70} -4.19018 q^{71} +2.99990 q^{72} +10.6965 q^{73} +3.78473 q^{74} +0.0459124 q^{75} -6.48034 q^{77} +0.0105065 q^{78} -10.7217 q^{79} -3.08958 q^{80} +8.99908 q^{81} -6.35887 q^{82} -6.72185 q^{83} +0.0101006 q^{84} -7.76769 q^{85} -1.33133 q^{86} -0.0527245 q^{87} +6.48034 q^{88} -2.05416 q^{89} -9.26844 q^{90} -1.04019 q^{91} -8.22045 q^{92} -0.0830477 q^{93} +2.96047 q^{94} -0.0101006 q^{96} +18.9122 q^{97} -1.00000 q^{98} +19.4404 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

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