LMFDB - Embedded newform 5054.2.a.bh.1.8

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:	$8$
Coefficient field:	8.8.19520000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 $ x^8 - 2x^7 - 12x^6 + 16x^5 + 50x^4 - 24x^3 - 72x^2 - 32*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.35877$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.35992 q^{3} +1.00000 q^{4} -4.10066 q^{5} +2.35992 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.56920 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.35992 q^{3} +1.00000 q^{4} -4.10066 q^{5} +2.35992 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.56920 q^{9} -4.10066 q^{10} -2.03351 q^{11} +2.35992 q^{12} -5.49067 q^{13} +1.00000 q^{14} -9.67721 q^{15} +1.00000 q^{16} +6.00566 q^{17} +2.56920 q^{18} -4.10066 q^{20} +2.35992 q^{21} -2.03351 q^{22} +1.22079 q^{23} +2.35992 q^{24} +11.8154 q^{25} -5.49067 q^{26} -1.01664 q^{27} +1.00000 q^{28} -3.38352 q^{29} -9.67721 q^{30} -2.41661 q^{31} +1.00000 q^{32} -4.79891 q^{33} +6.00566 q^{34} -4.10066 q^{35} +2.56920 q^{36} -8.56204 q^{37} -12.9575 q^{39} -4.10066 q^{40} +1.69201 q^{41} +2.35992 q^{42} -10.3750 q^{43} -2.03351 q^{44} -10.5354 q^{45} +1.22079 q^{46} -10.7789 q^{47} +2.35992 q^{48} +1.00000 q^{49} +11.8154 q^{50} +14.1729 q^{51} -5.49067 q^{52} -9.20307 q^{53} -1.01664 q^{54} +8.33871 q^{55} +1.00000 q^{56} -3.38352 q^{58} -0.753523 q^{59} -9.67721 q^{60} -1.75467 q^{61} -2.41661 q^{62} +2.56920 q^{63} +1.00000 q^{64} +22.5154 q^{65} -4.79891 q^{66} +5.87511 q^{67} +6.00566 q^{68} +2.88097 q^{69} -4.10066 q^{70} -4.12251 q^{71} +2.56920 q^{72} +12.9646 q^{73} -8.56204 q^{74} +27.8833 q^{75} -2.03351 q^{77} -12.9575 q^{78} -12.6425 q^{79} -4.10066 q^{80} -10.1068 q^{81} +1.69201 q^{82} -5.55170 q^{83} +2.35992 q^{84} -24.6272 q^{85} -10.3750 q^{86} -7.98482 q^{87} -2.03351 q^{88} +15.6749 q^{89} -10.5354 q^{90} -5.49067 q^{91} +1.22079 q^{92} -5.70301 q^{93} -10.7789 q^{94} +2.35992 q^{96} +9.13311 q^{97} +1.00000 q^{98} -5.22449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9} - 2 q^{10} - 12 q^{11} - 4 q^{12} - 10 q^{13} + 8 q^{14} - 24 q^{15} + 8 q^{16} - 6 q^{17} + 8 q^{18} - 2 q^{20} - 4 q^{21} - 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} - 22 q^{27} + 8 q^{28} - 8 q^{29} - 24 q^{30} - 18 q^{31} + 8 q^{32} + 16 q^{33} - 6 q^{34} - 2 q^{35} + 8 q^{36} - 36 q^{37} - 2 q^{40} - 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} - 20 q^{46} - 10 q^{47} - 4 q^{48} + 8 q^{49} + 8 q^{50} - 12 q^{51} - 10 q^{52} - 32 q^{53} - 22 q^{54} - 22 q^{55} + 8 q^{56} - 8 q^{58} + 2 q^{59} - 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} - 44 q^{67} - 6 q^{68} - 2 q^{70} - 8 q^{71} + 8 q^{72} + 30 q^{73} - 36 q^{74} + 16 q^{75} - 12 q^{77} - 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} - 4 q^{84} - 16 q^{85} - 16 q^{86} + 24 q^{87} - 12 q^{88} + 22 q^{89} + 8 q^{90} - 10 q^{91} - 20 q^{92} - 16 q^{93} - 10 q^{94} - 4 q^{96} + 6 q^{97} + 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 + 8 * q^8 + 8 * q^9 - 2 * q^10 - 12 * q^11 - 4 * q^12 - 10 * q^13 + 8 * q^14 - 24 * q^15 + 8 * q^16 - 6 * q^17 + 8 * q^18 - 2 * q^20 - 4 * q^21 - 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 - 22 * q^27 + 8 * q^28 - 8 * q^29 - 24 * q^30 - 18 * q^31 + 8 * q^32 + 16 * q^33 - 6 * q^34 - 2 * q^35 + 8 * q^36 - 36 * q^37 - 2 * q^40 - 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 - 20 * q^46 - 10 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 - 12 * q^51 - 10 * q^52 - 32 * q^53 - 22 * q^54 - 22 * q^55 + 8 * q^56 - 8 * q^58 + 2 * q^59 - 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 - 44 * q^67 - 6 * q^68 - 2 * q^70 - 8 * q^71 + 8 * q^72 + 30 * q^73 - 36 * q^74 + 16 * q^75 - 12 * q^77 - 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 - 4 * q^84 - 16 * q^85 - 16 * q^86 + 24 * q^87 - 12 * q^88 + 22 * q^89 + 8 * q^90 - 10 * q^91 - 20 * q^92 - 16 * q^93 - 10 * q^94 - 4 * q^96 + 6 * q^97 + 8 * q^98 - 52 * 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
$3$	2.35992	1.36250	0.681249	−	0.732052i	$-0.261437\pi$
$3$	2.35992	1.36250	0.681249	+	0.732052i	$0.261437\pi$
$4$	1.00000	0.500000
$5$	−4.10066	−1.83387	−0.916935	−	0.399037i	$-0.869344\pi$
$5$	−4.10066	−1.83387	−0.916935	+	0.399037i	$0.869344\pi$
$6$	2.35992	0.963432
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	2.56920	0.856401
$10$	−4.10066	−1.29674
$11$	−2.03351	−0.613125	−0.306563	−	0.951850i	$-0.599179\pi$
$11$	−2.03351	−0.613125	−0.306563	+	0.951850i	$0.599179\pi$
$12$	2.35992	0.681249
$13$	−5.49067	−1.52284	−0.761419	−	0.648260i	$-0.775497\pi$
$13$	−5.49067	−1.52284	−0.761419	+	0.648260i	$0.775497\pi$
$14$	1.00000	0.267261
$15$	−9.67721	−2.49864
$16$	1.00000	0.250000
$17$	6.00566	1.45659	0.728294	−	0.685265i	$-0.240314\pi$
$17$	6.00566	1.45659	0.728294	+	0.685265i	$0.240314\pi$
$18$	2.56920	0.605567
$19$	0	0
$19$	0	0
$20$	−4.10066	−0.916935
$21$	2.35992	0.514976
$22$	−2.03351	−0.433545
$23$	1.22079	0.254553	0.127276	−	0.991867i	$-0.459376\pi$
$23$	1.22079	0.254553	0.127276	+	0.991867i	$0.459376\pi$
$24$	2.35992	0.481716
$25$	11.8154	2.36308
$26$	−5.49067	−1.07681
$27$	−1.01664	−0.195653
$28$	1.00000	0.188982
$29$	−3.38352	−0.628303	−0.314152	−	0.949373i	$-0.601720\pi$
$29$	−3.38352	−0.628303	−0.314152	+	0.949373i	$0.601720\pi$
$30$	−9.67721	−1.76681
$31$	−2.41661	−0.434037	−0.217018	−	0.976168i	$-0.569633\pi$
$31$	−2.41661	−0.434037	−0.217018	+	0.976168i	$0.569633\pi$
$32$	1.00000	0.176777
$33$	−4.79891	−0.835382
$34$	6.00566	1.02996
$35$	−4.10066	−0.693138
$36$	2.56920	0.428201
$37$	−8.56204	−1.40759	−0.703795	−	0.710403i	$-0.748513\pi$
$37$	−8.56204	−1.40759	−0.703795	+	0.710403i	$0.748513\pi$
$38$	0	0
$39$	−12.9575	−2.07487
$40$	−4.10066	−0.648371
$41$	1.69201	0.264247	0.132123	−	0.991233i	$-0.457820\pi$
$41$	1.69201	0.264247	0.132123	+	0.991233i	$0.457820\pi$
$42$	2.35992	0.364143
$43$	−10.3750	−1.58217	−0.791084	−	0.611707i	$-0.790483\pi$
$43$	−10.3750	−1.58217	−0.791084	+	0.611707i	$0.790483\pi$
$44$	−2.03351	−0.306563
$45$	−10.5354	−1.57053
$46$	1.22079	0.179996
$47$	−10.7789	−1.57227	−0.786133	−	0.618057i	$-0.787920\pi$
$47$	−10.7789	−1.57227	−0.786133	+	0.618057i	$0.787920\pi$
$48$	2.35992	0.340625
$49$	1.00000	0.142857
$50$	11.8154	1.67095
$51$	14.1729	1.98460
$52$	−5.49067	−0.761419
$53$	−9.20307	−1.26414	−0.632069	−	0.774912i	$-0.717794\pi$
$53$	−9.20307	−1.26414	−0.632069	+	0.774912i	$0.717794\pi$
$54$	−1.01664	−0.138348
$55$	8.33871	1.12439
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.38352	−0.444278
$59$	−0.753523	−0.0981004	−0.0490502	−	0.998796i	$-0.515619\pi$
$59$	−0.753523	−0.0981004	−0.0490502	+	0.998796i	$0.515619\pi$
$60$	−9.67721	−1.24932
$61$	−1.75467	−0.224663	−0.112332	−	0.993671i	$-0.535832\pi$
$61$	−1.75467	−0.224663	−0.112332	+	0.993671i	$0.535832\pi$
$62$	−2.41661	−0.306910
$63$	2.56920	0.323689
$64$	1.00000	0.125000
$65$	22.5154	2.79269
$66$	−4.79891	−0.590704
$67$	5.87511	0.717759	0.358880	−	0.933384i	$-0.383159\pi$
$67$	5.87511	0.717759	0.358880	+	0.933384i	$0.383159\pi$
$68$	6.00566	0.728294
$69$	2.88097	0.346828
$70$	−4.10066	−0.490122
$71$	−4.12251	−0.489252	−0.244626	−	0.969618i	$-0.578665\pi$
$71$	−4.12251	−0.489252	−0.244626	+	0.969618i	$0.578665\pi$
$72$	2.56920	0.302784
$73$	12.9646	1.51739	0.758695	−	0.651446i	$-0.225837\pi$
$73$	12.9646	1.51739	0.758695	+	0.651446i	$0.225837\pi$
$74$	−8.56204	−0.995317
$75$	27.8833	3.21969
$76$	0	0
$77$	−2.03351	−0.231740
$78$	−12.9575	−1.46715
$79$	−12.6425	−1.42240	−0.711199	−	0.702991i	$-0.751847\pi$
$79$	−12.6425	−1.42240	−0.711199	+	0.702991i	$0.751847\pi$
$80$	−4.10066	−0.458467
$81$	−10.1068	−1.12298
$82$	1.69201	0.186851
$83$	−5.55170	−0.609379	−0.304689	−	0.952452i	$-0.598553\pi$
$83$	−5.55170	−0.609379	−0.304689	+	0.952452i	$0.598553\pi$
$84$	2.35992	0.257488
$85$	−24.6272	−2.67119
$86$	−10.3750	−1.11876
$87$	−7.98482	−0.856062
$88$	−2.03351	−0.216773
$89$	15.6749	1.66154	0.830770	−	0.556616i	$-0.187900\pi$
$89$	15.6749	1.66154	0.830770	+	0.556616i	$0.187900\pi$
$90$	−10.5354	−1.11053
$91$	−5.49067	−0.575579
$92$	1.22079	0.127276
$93$	−5.70301	−0.591374
$94$	−10.7789	−1.11176
$95$	0	0
$96$	2.35992	0.240858
$97$	9.13311	0.927327	0.463664	−	0.886011i	$-0.346535\pi$
$97$	9.13311	0.927327	0.463664	+	0.886011i	$0.346535\pi$
$98$	1.00000	0.101015
$99$	−5.22449	−0.525081
$100$	11.8154	1.18154
$101$	9.18698	0.914139	0.457069	−	0.889431i	$-0.348899\pi$
$101$	9.18698	0.914139	0.457069	+	0.889431i	$0.348899\pi$
$102$	14.1729	1.40332
$103$	−9.89474	−0.974958	−0.487479	−	0.873135i	$-0.662083\pi$
$103$	−9.89474	−0.974958	−0.487479	+	0.873135i	$0.662083\pi$
$104$	−5.49067	−0.538405
$105$	−9.67721	−0.944399
$106$	−9.20307	−0.893881
$107$	−2.46875	−0.238663	−0.119331	−	0.992854i	$-0.538075\pi$
$107$	−2.46875	−0.238663	−0.119331	+	0.992854i	$0.538075\pi$
$108$	−1.01664	−0.0978265
$109$	5.03056	0.481840	0.240920	−	0.970545i	$-0.422551\pi$
$109$	5.03056	0.481840	0.240920	+	0.970545i	$0.422551\pi$
$110$	8.33871	0.795065
$111$	−20.2057	−1.91784
$112$	1.00000	0.0944911
$113$	−13.9823	−1.31535	−0.657673	−	0.753304i	$-0.728459\pi$
$113$	−13.9823	−1.31535	−0.657673	+	0.753304i	$0.728459\pi$
$114$	0	0
$115$	−5.00605	−0.466817
$116$	−3.38352	−0.314152
$117$	−14.1067	−1.30416
$118$	−0.753523	−0.0693674
$119$	6.00566	0.550538
$120$	−9.67721	−0.883404
$121$	−6.86485	−0.624077
$122$	−1.75467	−0.158861
$123$	3.99299	0.360036
$124$	−2.41661	−0.217018
$125$	−27.9476	−2.49971
$126$	2.56920	0.228883
$127$	−17.4412	−1.54766	−0.773828	−	0.633395i	$-0.781661\pi$
$127$	−17.4412	−1.54766	−0.773828	+	0.633395i	$0.781661\pi$
$128$	1.00000	0.0883883
$129$	−24.4841	−2.15570
$130$	22.5154	1.97473
$131$	−22.6819	−1.98173	−0.990864	−	0.134862i	$-0.956941\pi$
$131$	−22.6819	−1.98173	−0.990864	+	0.134862i	$0.956941\pi$
$132$	−4.79891	−0.417691
$133$	0	0
$134$	5.87511	0.507533
$135$	4.16890	0.358802
$136$	6.00566	0.514981
$137$	4.90621	0.419166	0.209583	−	0.977791i	$-0.432789\pi$
$137$	4.90621	0.419166	0.209583	+	0.977791i	$0.432789\pi$
$138$	2.88097	0.245244
$139$	−17.2424	−1.46248	−0.731241	−	0.682119i	$-0.761058\pi$
$139$	−17.2424	−1.46248	−0.731241	+	0.682119i	$0.761058\pi$
$140$	−4.10066	−0.346569
$141$	−25.4373	−2.14221
$142$	−4.12251	−0.345953
$143$	11.1653	0.933691
$144$	2.56920	0.214100
$145$	13.8746	1.15223
$146$	12.9646	1.07296
$147$	2.35992	0.194643
$148$	−8.56204	−0.703795
$149$	18.9520	1.55261	0.776306	−	0.630357i	$-0.217091\pi$
$149$	18.9520	1.55261	0.776306	+	0.630357i	$0.217091\pi$
$150$	27.8833	2.27666
$151$	−4.09962	−0.333623	−0.166811	−	0.985989i	$-0.553347\pi$
$151$	−4.09962	−0.333623	−0.166811	+	0.985989i	$0.553347\pi$
$152$	0	0
$153$	15.4298	1.24742
$154$	−2.03351	−0.163865
$155$	9.90971	0.795967
$156$	−12.9575	−1.03743
$157$	11.3041	0.902166	0.451083	−	0.892482i	$-0.351038\pi$
$157$	11.3041	0.902166	0.451083	+	0.892482i	$0.351038\pi$
$158$	−12.6425	−1.00579
$159$	−21.7185	−1.72239
$160$	−4.10066	−0.324185
$161$	1.22079	0.0962120
$162$	−10.1068	−0.794065
$163$	−3.25499	−0.254950	−0.127475	−	0.991842i	$-0.540687\pi$
$163$	−3.25499	−0.254950	−0.127475	+	0.991842i	$0.540687\pi$
$164$	1.69201	0.132123
$165$	19.6787	1.53198
$166$	−5.55170	−0.430896
$167$	−1.99367	−0.154275	−0.0771375	−	0.997020i	$-0.524578\pi$
$167$	−1.99367	−0.154275	−0.0771375	+	0.997020i	$0.524578\pi$
$168$	2.35992	0.182071
$169$	17.1475	1.31904
$170$	−24.6272	−1.88882
$171$	0	0
$172$	−10.3750	−0.791084
$173$	23.5491	1.79041	0.895203	−	0.445659i	$-0.147031\pi$
$173$	23.5491	1.79041	0.895203	+	0.445659i	$0.147031\pi$
$174$	−7.98482	−0.605327
$175$	11.8154	0.893159
$176$	−2.03351	−0.153281
$177$	−1.77825	−0.133662
$178$	15.6749	1.17489
$179$	−1.78906	−0.133721	−0.0668604	−	0.997762i	$-0.521298\pi$
$179$	−1.78906	−0.133721	−0.0668604	+	0.997762i	$0.521298\pi$
$180$	−10.5354	−0.785264
$181$	1.95922	0.145628	0.0728138	−	0.997346i	$-0.476802\pi$
$181$	1.95922	0.145628	0.0728138	+	0.997346i	$0.476802\pi$
$182$	−5.49067	−0.406996
$183$	−4.14088	−0.306103
$184$	1.22079	0.0899980
$185$	35.1100	2.58134
$186$	−5.70301	−0.418165
$187$	−12.2126	−0.893070
$188$	−10.7789	−0.786133
$189$	−1.01664	−0.0739499
$190$	0	0
$191$	0.753847	0.0545464	0.0272732	−	0.999628i	$-0.491318\pi$
$191$	0.753847	0.0545464	0.0272732	+	0.999628i	$0.491318\pi$
$192$	2.35992	0.170312
$193$	6.31071	0.454255	0.227127	−	0.973865i	$-0.427067\pi$
$193$	6.31071	0.454255	0.227127	+	0.973865i	$0.427067\pi$
$194$	9.13311	0.655719
$195$	53.1344	3.80503
$196$	1.00000	0.0714286
$197$	−11.7879	−0.839852	−0.419926	−	0.907558i	$-0.637944\pi$
$197$	−11.7879	−0.839852	−0.419926	+	0.907558i	$0.637944\pi$
$198$	−5.22449	−0.371289
$199$	16.2045	1.14871	0.574354	−	0.818607i	$-0.305253\pi$
$199$	16.2045	1.14871	0.574354	+	0.818607i	$0.305253\pi$
$200$	11.8154	0.835474
$201$	13.8648	0.977946
$202$	9.18698	0.646394
$203$	−3.38352	−0.237476
$204$	14.1729	0.992299
$205$	−6.93834	−0.484594
$206$	−9.89474	−0.689399
$207$	3.13647	0.217999
$208$	−5.49067	−0.380710
$209$	0	0
$210$	−9.67721	−0.667791
$211$	−8.28584	−0.570421	−0.285210	−	0.958465i	$-0.592063\pi$
$211$	−8.28584	−0.570421	−0.285210	+	0.958465i	$0.592063\pi$
$212$	−9.20307	−0.632069
$213$	−9.72877	−0.666604
$214$	−2.46875	−0.168760
$215$	42.5442	2.90149
$216$	−1.01664	−0.0691738
$217$	−2.41661	−0.164050
$218$	5.03056	0.340713
$219$	30.5953	2.06744
$220$	8.33871	0.562196
$221$	−32.9751	−2.21815
$222$	−20.2057	−1.35612
$223$	11.0275	0.738455	0.369228	−	0.929339i	$-0.379622\pi$
$223$	11.0275	0.738455	0.369228	+	0.929339i	$0.379622\pi$
$224$	1.00000	0.0668153
$225$	30.3561	2.02374
$226$	−13.9823	−0.930090
$227$	13.6062	0.903075	0.451537	−	0.892252i	$-0.350876\pi$
$227$	13.6062	0.903075	0.451537	+	0.892252i	$0.350876\pi$
$228$	0	0
$229$	−18.7842	−1.24129	−0.620647	−	0.784090i	$-0.713130\pi$
$229$	−18.7842	−1.24129	−0.620647	+	0.784090i	$0.713130\pi$
$230$	−5.00605	−0.330089
$231$	−4.79891	−0.315745
$232$	−3.38352	−0.222139
$233$	1.29417	0.0847836	0.0423918	−	0.999101i	$-0.486502\pi$
$233$	1.29417	0.0847836	0.0423918	+	0.999101i	$0.486502\pi$
$234$	−14.1067	−0.922181
$235$	44.2006	2.88333
$236$	−0.753523	−0.0490502
$237$	−29.8354	−1.93801
$238$	6.00566	0.389289
$239$	0.889440	0.0575331	0.0287665	−	0.999586i	$-0.490842\pi$
$239$	0.889440	0.0575331	0.0287665	+	0.999586i	$0.490842\pi$
$240$	−9.67721	−0.624661
$241$	−29.3776	−1.89238	−0.946188	−	0.323618i	$-0.895101\pi$
$241$	−29.3776	−1.89238	−0.946188	+	0.323618i	$0.895101\pi$
$242$	−6.86485	−0.441289
$243$	−20.8013	−1.33440
$244$	−1.75467	−0.112332
$245$	−4.10066	−0.261981
$246$	3.99299	0.254584
$247$	0	0
$248$	−2.41661	−0.153455
$249$	−13.1016	−0.830277
$250$	−27.9476	−1.76756
$251$	28.7724	1.81610	0.908050	−	0.418862i	$-0.137571\pi$
$251$	28.7724	1.81610	0.908050	+	0.418862i	$0.137571\pi$
$252$	2.56920	0.161845
$253$	−2.48249	−0.156073
$254$	−17.4412	−1.09436
$255$	−58.1180	−3.63949
$256$	1.00000	0.0625000
$257$	12.8359	0.800683	0.400341	−	0.916366i	$-0.368892\pi$
$257$	12.8359	0.800683	0.400341	+	0.916366i	$0.368892\pi$
$258$	−24.4841	−1.52431
$259$	−8.56204	−0.532019
$260$	22.5154	1.39634
$261$	−8.69294	−0.538080
$262$	−22.6819	−1.40129
$263$	15.0217	0.926277	0.463138	−	0.886286i	$-0.346723\pi$
$263$	15.0217	0.926277	0.463138	+	0.886286i	$0.346723\pi$
$264$	−4.79891	−0.295352
$265$	37.7386	2.31826
$266$	0	0
$267$	36.9915	2.26385
$268$	5.87511	0.358880
$269$	−5.41016	−0.329864	−0.164932	−	0.986305i	$-0.552740\pi$
$269$	−5.41016	−0.329864	−0.164932	+	0.986305i	$0.552740\pi$
$270$	4.16890	0.253711
$271$	19.5591	1.18813	0.594065	−	0.804417i	$-0.297522\pi$
$271$	19.5591	1.18813	0.594065	+	0.804417i	$0.297522\pi$
$272$	6.00566	0.364147
$273$	−12.9575	−0.784225
$274$	4.90621	0.296395
$275$	−24.0267	−1.44886
$276$	2.88097	0.173414
$277$	17.1255	1.02897	0.514486	−	0.857499i	$-0.327983\pi$
$277$	17.1255	1.02897	0.514486	+	0.857499i	$0.327983\pi$
$278$	−17.2424	−1.03413
$279$	−6.20877	−0.371710
$280$	−4.10066	−0.245061
$281$	−14.9194	−0.890014	−0.445007	−	0.895527i	$-0.646799\pi$
$281$	−14.9194	−0.890014	−0.445007	+	0.895527i	$0.646799\pi$
$282$	−25.4373	−1.51477
$283$	−13.5587	−0.805979	−0.402990	−	0.915205i	$-0.632029\pi$
$283$	−13.5587	−0.805979	−0.402990	+	0.915205i	$0.632029\pi$
$284$	−4.12251	−0.244626
$285$	0	0
$286$	11.1653	0.660219
$287$	1.69201	0.0998760
$288$	2.56920	0.151392
$289$	19.0680	1.12165
$290$	13.8746	0.814747
$291$	21.5534	1.26348
$292$	12.9646	0.758695
$293$	7.15378	0.417928	0.208964	−	0.977923i	$-0.432991\pi$
$293$	7.15378	0.417928	0.208964	+	0.977923i	$0.432991\pi$
$294$	2.35992	0.137633
$295$	3.08994	0.179903
$296$	−8.56204	−0.497659
$297$	2.06735	0.119960
$298$	18.9520	1.09786
$299$	−6.70298	−0.387643
$300$	27.8833	1.60984
$301$	−10.3750	−0.598004
$302$	−4.09962	−0.235907
$303$	21.6805	1.24551
$304$	0	0
$305$	7.19532	0.412003
$306$	15.4298	0.882061
$307$	33.0384	1.88560	0.942801	−	0.333355i	$-0.108181\pi$
$307$	33.0384	1.88560	0.942801	+	0.333355i	$0.108181\pi$
$308$	−2.03351	−0.115870
$309$	−23.3508	−1.32838
$310$	9.90971	0.562833
$311$	1.17172	0.0664421	0.0332210	−	0.999448i	$-0.489423\pi$
$311$	1.17172	0.0664421	0.0332210	+	0.999448i	$0.489423\pi$
$312$	−12.9575	−0.733576
$313$	−6.66348	−0.376642	−0.188321	−	0.982108i	$-0.560305\pi$
$313$	−6.66348	−0.376642	−0.188321	+	0.982108i	$0.560305\pi$
$314$	11.3041	0.637928
$315$	−10.5354	−0.593604
$316$	−12.6425	−0.711199
$317$	10.9920	0.617372	0.308686	−	0.951164i	$-0.400111\pi$
$317$	10.9920	0.617372	0.308686	+	0.951164i	$0.400111\pi$
$318$	−21.7185	−1.21791
$319$	6.88040	0.385229
$320$	−4.10066	−0.229234
$321$	−5.82604	−0.325178
$322$	1.22079	0.0680321
$323$	0	0
$324$	−10.1068	−0.561489
$325$	−64.8744	−3.59859
$326$	−3.25499	−0.180277
$327$	11.8717	0.656506
$328$	1.69201	0.0934254
$329$	−10.7789	−0.594261
$330$	19.6787	1.08327
$331$	−11.2710	−0.619513	−0.309756	−	0.950816i	$-0.600247\pi$
$331$	−11.2710	−0.619513	−0.309756	+	0.950816i	$0.600247\pi$
$332$	−5.55170	−0.304689
$333$	−21.9976	−1.20546
$334$	−1.99367	−0.109089
$335$	−24.0918	−1.31628
$336$	2.35992	0.128744
$337$	14.3044	0.779212	0.389606	−	0.920982i	$-0.372611\pi$
$337$	14.3044	0.779212	0.389606	+	0.920982i	$0.372611\pi$
$338$	17.1475	0.932701
$339$	−32.9971	−1.79216
$340$	−24.6272	−1.33560
$341$	4.91420	0.266119
$342$	0	0
$343$	1.00000	0.0539949
$344$	−10.3750	−0.559381
$345$	−11.8139	−0.636037
$346$	23.5491	1.26601
$347$	−5.22077	−0.280266	−0.140133	−	0.990133i	$-0.544753\pi$
$347$	−5.22077	−0.280266	−0.140133	+	0.990133i	$0.544753\pi$
$348$	−7.98482	−0.428031
$349$	15.4070	0.824719	0.412360	−	0.911021i	$-0.364705\pi$
$349$	15.4070	0.824719	0.412360	+	0.911021i	$0.364705\pi$
$350$	11.8154	0.631559
$351$	5.58205	0.297948
$352$	−2.03351	−0.108386
$353$	2.37291	0.126297	0.0631487	−	0.998004i	$-0.479886\pi$
$353$	2.37291	0.126297	0.0631487	+	0.998004i	$0.479886\pi$
$354$	−1.77825	−0.0945130
$355$	16.9050	0.897223
$356$	15.6749	0.830770
$357$	14.1729	0.750107
$358$	−1.78906	−0.0945549
$359$	10.3620	0.546883	0.273442	−	0.961889i	$-0.411838\pi$
$359$	10.3620	0.546883	0.273442	+	0.961889i	$0.411838\pi$
$360$	−10.5354	−0.555266
$361$	0	0
$362$	1.95922	0.102974
$363$	−16.2005	−0.850304
$364$	−5.49067	−0.287789
$365$	−53.1633	−2.78269
$366$	−4.14088	−0.216447
$367$	−19.9753	−1.04270	−0.521350	−	0.853343i	$-0.674571\pi$
$367$	−19.9753	−1.04270	−0.521350	+	0.853343i	$0.674571\pi$
$368$	1.22079	0.0636382
$369$	4.34711	0.226301
$370$	35.1100	1.82528
$371$	−9.20307	−0.477799
$372$	−5.70301	−0.295687
$373$	6.59897	0.341682	0.170841	−	0.985299i	$-0.445352\pi$
$373$	6.59897	0.341682	0.170841	+	0.985299i	$0.445352\pi$
$374$	−12.2126	−0.631496
$375$	−65.9539	−3.40585
$376$	−10.7789	−0.555880
$377$	18.5778	0.956805
$378$	−1.01664	−0.0522905
$379$	−31.9921	−1.64333	−0.821663	−	0.569974i	$-0.806953\pi$
$379$	−31.9921	−1.64333	−0.821663	+	0.569974i	$0.806953\pi$
$380$	0	0
$381$	−41.1598	−2.10868
$382$	0.753847	0.0385702
$383$	−0.351820	−0.0179772	−0.00898858	−	0.999960i	$-0.502861\pi$
$383$	−0.351820	−0.0179772	−0.00898858	+	0.999960i	$0.502861\pi$
$384$	2.35992	0.120429
$385$	8.33871	0.424980
$386$	6.31071	0.321207
$387$	−26.6554	−1.35497
$388$	9.13311	0.463664
$389$	−19.8365	−1.00575	−0.502876	−	0.864359i	$-0.667725\pi$
$389$	−19.8365	−1.00575	−0.502876	+	0.864359i	$0.667725\pi$
$390$	53.1344	2.69056
$391$	7.33167	0.370778
$392$	1.00000	0.0505076
$393$	−53.5274	−2.70010
$394$	−11.7879	−0.593865
$395$	51.8428	2.60849
$396$	−5.22449	−0.262541
$397$	18.6253	0.934775	0.467388	−	0.884052i	$-0.345195\pi$
$397$	18.6253	0.934775	0.467388	+	0.884052i	$0.345195\pi$
$398$	16.2045	0.812259
$399$	0	0
$400$	11.8154	0.590769
$401$	−15.2434	−0.761217	−0.380608	−	0.924736i	$-0.624285\pi$
$401$	−15.2434	−0.761217	−0.380608	+	0.924736i	$0.624285\pi$
$402$	13.8648	0.691512
$403$	13.2688	0.660968
$404$	9.18698	0.457069
$405$	41.4445	2.05940
$406$	−3.38352	−0.167921
$407$	17.4110	0.863030
$408$	14.1729	0.701661
$409$	−10.7468	−0.531393	−0.265696	−	0.964057i	$-0.585602\pi$
$409$	−10.7468	−0.531393	−0.265696	+	0.964057i	$0.585602\pi$
$410$	−6.93834	−0.342660
$411$	11.5783	0.571113
$412$	−9.89474	−0.487479
$413$	−0.753523	−0.0370784
$414$	3.13647	0.154149
$415$	22.7656	1.11752
$416$	−5.49067	−0.269202
$417$	−40.6906	−1.99263
$418$	0	0
$419$	30.5702	1.49345	0.746727	−	0.665131i	$-0.231624\pi$
$419$	30.5702	1.49345	0.746727	+	0.665131i	$0.231624\pi$
$420$	−9.67721	−0.472199
$421$	16.7182	0.814795	0.407397	−	0.913251i	$-0.366436\pi$
$421$	16.7182	0.814795	0.407397	+	0.913251i	$0.366436\pi$
$422$	−8.28584	−0.403348
$423$	−27.6932	−1.34649
$424$	−9.20307	−0.446940
$425$	70.9592	3.44203
$426$	−9.72877	−0.471360
$427$	−1.75467	−0.0849146
$428$	−2.46875	−0.119331
$429$	26.3492	1.27215
$430$	42.5442	2.05166
$431$	32.7077	1.57547	0.787737	−	0.616012i	$-0.211253\pi$
$431$	32.7077	1.57547	0.787737	+	0.616012i	$0.211253\pi$
$432$	−1.01664	−0.0489133
$433$	−4.86618	−0.233854	−0.116927	−	0.993141i	$-0.537304\pi$
$433$	−4.86618	−0.233854	−0.116927	+	0.993141i	$0.537304\pi$
$434$	−2.41661	−0.116001
$435$	32.7430	1.56991
$436$	5.03056	0.240920
$437$	0	0
$438$	30.5953	1.46190
$439$	6.27304	0.299396	0.149698	−	0.988732i	$-0.452170\pi$
$439$	6.27304	0.299396	0.149698	+	0.988732i	$0.452170\pi$
$440$	8.33871	0.397533
$441$	2.56920	0.122343
$442$	−32.9751	−1.56847
$443$	−1.73179	−0.0822797	−0.0411398	−	0.999153i	$-0.513099\pi$
$443$	−1.73179	−0.0822797	−0.0411398	+	0.999153i	$0.513099\pi$
$444$	−20.2057	−0.958920
$445$	−64.2776	−3.04705
$446$	11.0275	0.522167
$447$	44.7252	2.11543
$448$	1.00000	0.0472456
$449$	4.58054	0.216169	0.108084	−	0.994142i	$-0.465528\pi$
$449$	4.58054	0.216169	0.108084	+	0.994142i	$0.465528\pi$
$450$	30.3561	1.43100
$451$	−3.44071	−0.162017
$452$	−13.9823	−0.657673
$453$	−9.67477	−0.454560
$454$	13.6062	0.638570
$455$	22.5154	1.05554
$456$	0	0
$457$	9.34917	0.437336	0.218668	−	0.975799i	$-0.429829\pi$
$457$	9.34917	0.437336	0.218668	+	0.975799i	$0.429829\pi$
$458$	−18.7842	−0.877727
$459$	−6.10561	−0.284986
$460$	−5.00605	−0.233408
$461$	12.6825	0.590681	0.295341	−	0.955392i	$-0.404567\pi$
$461$	12.6825	0.590681	0.295341	+	0.955392i	$0.404567\pi$
$462$	−4.79891	−0.223265
$463$	−12.8438	−0.596901	−0.298450	−	0.954425i	$-0.596470\pi$
$463$	−12.8438	−0.596901	−0.298450	+	0.954425i	$0.596470\pi$
$464$	−3.38352	−0.157076
$465$	23.3861	1.08450
$466$	1.29417	0.0599511
$467$	−17.4065	−0.805479	−0.402739	−	0.915315i	$-0.631942\pi$
$467$	−17.4065	−0.805479	−0.402739	+	0.915315i	$0.631942\pi$
$468$	−14.1067	−0.652081
$469$	5.87511	0.271288
$470$	44.2006	2.03882
$471$	26.6767	1.22920
$472$	−0.753523	−0.0346837
$473$	21.0976	0.970068
$474$	−29.8354	−1.37038
$475$	0	0
$476$	6.00566	0.275269
$477$	−23.6446	−1.08261
$478$	0.889440	0.0406820
$479$	−15.5581	−0.710869	−0.355434	−	0.934701i	$-0.615667\pi$
$479$	−15.5581	−0.710869	−0.355434	+	0.934701i	$0.615667\pi$
$480$	−9.67721	−0.441702
$481$	47.0114	2.14353
$482$	−29.3776	−1.33811
$483$	2.88097	0.131089
$484$	−6.86485	−0.312039
$485$	−37.4518	−1.70060
$486$	−20.8013	−0.943565
$487$	−2.88504	−0.130734	−0.0653668	−	0.997861i	$-0.520822\pi$
$487$	−2.88504	−0.130734	−0.0653668	+	0.997861i	$0.520822\pi$
$488$	−1.75467	−0.0794304
$489$	−7.68150	−0.347369
$490$	−4.10066	−0.185249
$491$	7.75242	0.349862	0.174931	−	0.984581i	$-0.444030\pi$
$491$	7.75242	0.349862	0.174931	+	0.984581i	$0.444030\pi$
$492$	3.99299	0.180018
$493$	−20.3203	−0.915178
$494$	0	0
$495$	21.4239	0.962931
$496$	−2.41661	−0.108509
$497$	−4.12251	−0.184920
$498$	−13.1016	−0.587095
$499$	29.5766	1.32403	0.662015	−	0.749491i	$-0.269702\pi$
$499$	29.5766	1.32403	0.662015	+	0.749491i	$0.269702\pi$
$500$	−27.9476	−1.24985
$501$	−4.70490	−0.210199
$502$	28.7724	1.28418
$503$	29.7846	1.32803	0.664016	−	0.747719i	$-0.268851\pi$
$503$	29.7846	1.32803	0.664016	+	0.747719i	$0.268851\pi$
$504$	2.56920	0.114441
$505$	−37.6726	−1.67641
$506$	−2.48249	−0.110360
$507$	40.4667	1.79719
$508$	−17.4412	−0.773828
$509$	10.2339	0.453608	0.226804	−	0.973940i	$-0.427172\pi$
$509$	10.2339	0.453608	0.226804	+	0.973940i	$0.427172\pi$
$510$	−58.1180	−2.57351
$511$	12.9646	0.573519
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.8359	0.566168
$515$	40.5749	1.78795
$516$	−24.4841	−1.07785
$517$	21.9190	0.963997
$518$	−8.56204	−0.376194
$519$	55.5739	2.43942
$520$	22.5154	0.987364
$521$	−2.06594	−0.0905103	−0.0452551	−	0.998975i	$-0.514410\pi$
$521$	−2.06594	−0.0905103	−0.0452551	+	0.998975i	$0.514410\pi$
$522$	−8.69294	−0.380480
$523$	−36.1514	−1.58079	−0.790396	−	0.612596i	$-0.790125\pi$
$523$	−36.1514	−1.58079	−0.790396	+	0.612596i	$0.790125\pi$
$524$	−22.6819	−0.990864
$525$	27.8833	1.21693
$526$	15.0217	0.654977
$527$	−14.5134	−0.632212
$528$	−4.79891	−0.208846
$529$	−21.5097	−0.935203
$530$	37.7386	1.63926
$531$	−1.93595	−0.0840133
$532$	0	0
$533$	−9.29025	−0.402406
$534$	36.9915	1.60078
$535$	10.1235	0.437677
$536$	5.87511	0.253766
$537$	−4.22204	−0.182194
$538$	−5.41016	−0.233249
$539$	−2.03351	−0.0875893
$540$	4.16890	0.179401
$541$	−28.2453	−1.21436	−0.607181	−	0.794563i	$-0.707700\pi$
$541$	−28.2453	−1.21436	−0.607181	+	0.794563i	$0.707700\pi$
$542$	19.5591	0.840135
$543$	4.62359	0.198417
$544$	6.00566	0.257491
$545$	−20.6286	−0.883632
$546$	−12.9575	−0.554531
$547$	−43.9020	−1.87712	−0.938558	−	0.345122i	$-0.887838\pi$
$547$	−43.9020	−1.87712	−0.938558	+	0.345122i	$0.887838\pi$
$548$	4.90621	0.209583
$549$	−4.50812	−0.192402
$550$	−24.0267	−1.02450
$551$	0	0
$552$	2.88097	0.122622
$553$	−12.6425	−0.537616
$554$	17.1255	0.727593
$555$	82.8566	3.51707
$556$	−17.2424	−0.731241
$557$	12.1768	0.515946	0.257973	−	0.966152i	$-0.416945\pi$
$557$	12.1768	0.515946	0.257973	+	0.966152i	$0.416945\pi$
$558$	−6.20877	−0.262838
$559$	56.9656	2.40939
$560$	−4.10066	−0.173284
$561$	−28.8206	−1.21681
$562$	−14.9194	−0.629335
$563$	−19.2873	−0.812862	−0.406431	−	0.913682i	$-0.633227\pi$
$563$	−19.2873	−0.812862	−0.406431	+	0.913682i	$0.633227\pi$
$564$	−25.4373	−1.07111
$565$	57.3367	2.41217
$566$	−13.5587	−0.569913
$567$	−10.1068	−0.424446
$568$	−4.12251	−0.172977
$569$	−6.11324	−0.256280	−0.128140	−	0.991756i	$-0.540901\pi$
$569$	−6.11324	−0.256280	−0.128140	+	0.991756i	$0.540901\pi$
$570$	0	0
$571$	4.40580	0.184377	0.0921885	−	0.995742i	$-0.470614\pi$
$571$	4.40580	0.184377	0.0921885	+	0.995742i	$0.470614\pi$
$572$	11.1653	0.466846
$573$	1.77902	0.0743194
$574$	1.69201	0.0706230
$575$	14.4241	0.601528
$576$	2.56920	0.107050
$577$	−6.68034	−0.278106	−0.139053	−	0.990285i	$-0.544406\pi$
$577$	−6.68034	−0.278106	−0.139053	+	0.990285i	$0.544406\pi$
$578$	19.0680	0.793123
$579$	14.8927	0.618921
$580$	13.8746	0.576113
$581$	−5.55170	−0.230323
$582$	21.5534	0.893416
$583$	18.7145	0.775075
$584$	12.9646	0.536478
$585$	57.8466	2.39166
$586$	7.15378	0.295520
$587$	−33.9887	−1.40286	−0.701432	−	0.712737i	$-0.747455\pi$
$587$	−33.9887	−1.40286	−0.701432	+	0.712737i	$0.747455\pi$
$588$	2.35992	0.0973213
$589$	0	0
$590$	3.08994	0.127211
$591$	−27.8184	−1.14430
$592$	−8.56204	−0.351898
$593$	6.17527	0.253588	0.126794	−	0.991929i	$-0.459531\pi$
$593$	6.17527	0.253588	0.126794	+	0.991929i	$0.459531\pi$
$594$	2.06735	0.0848244
$595$	−24.6272	−1.00962
$596$	18.9520	0.776306
$597$	38.2413	1.56511
$598$	−6.70298	−0.274105
$599$	18.4899	0.755476	0.377738	−	0.925913i	$-0.376702\pi$
$599$	18.4899	0.755476	0.377738	+	0.925913i	$0.376702\pi$
$600$	27.8833	1.13833
$601$	−7.13452	−0.291023	−0.145512	−	0.989357i	$-0.546483\pi$
$601$	−7.13452	−0.291023	−0.145512	+	0.989357i	$0.546483\pi$
$602$	−10.3750	−0.422852
$603$	15.0944	0.614690
$604$	−4.09962	−0.166811
$605$	28.1504	1.14448
$606$	21.6805	0.880710
$607$	−14.8957	−0.604597	−0.302298	−	0.953213i	$-0.597754\pi$
$607$	−14.8957	−0.604597	−0.302298	+	0.953213i	$0.597754\pi$
$608$	0	0
$609$	−7.98482	−0.323561
$610$	7.19532	0.291330
$611$	59.1835	2.39431
$612$	15.4298	0.623711
$613$	−29.9531	−1.20979	−0.604897	−	0.796304i	$-0.706786\pi$
$613$	−29.9531	−1.20979	−0.604897	+	0.796304i	$0.706786\pi$
$614$	33.0384	1.33332
$615$	−16.3739	−0.660259
$616$	−2.03351	−0.0819323
$617$	23.7312	0.955381	0.477691	−	0.878528i	$-0.341474\pi$
$617$	23.7312	0.955381	0.477691	+	0.878528i	$0.341474\pi$
$618$	−23.3508	−0.939305
$619$	0.366291	0.0147225	0.00736125	−	0.999973i	$-0.497657\pi$
$619$	0.366291	0.0147225	0.00736125	+	0.999973i	$0.497657\pi$
$620$	9.90971	0.397983
$621$	−1.24111	−0.0498040
$622$	1.17172	0.0469816
$623$	15.6749	0.628003
$624$	−12.9575	−0.518716
$625$	55.5264	2.22106
$626$	−6.66348	−0.266326
$627$	0	0
$628$	11.3041	0.451083
$629$	−51.4207	−2.05028
$630$	−10.5354	−0.419741
$631$	1.95056	0.0776504	0.0388252	−	0.999246i	$-0.487638\pi$
$631$	1.95056	0.0776504	0.0388252	+	0.999246i	$0.487638\pi$
$632$	−12.6425	−0.502894
$633$	−19.5539	−0.777197
$634$	10.9920	0.436548
$635$	71.5204	2.83820
$636$	−21.7185	−0.861193
$637$	−5.49067	−0.217548
$638$	6.88040	0.272398
$639$	−10.5916	−0.418996
$640$	−4.10066	−0.162093
$641$	−45.7467	−1.80689	−0.903444	−	0.428706i	$-0.858970\pi$
$641$	−45.7467	−1.80689	−0.903444	+	0.428706i	$0.858970\pi$
$642$	−5.82604	−0.229935
$643$	−18.6775	−0.736567	−0.368284	−	0.929713i	$-0.620054\pi$
$643$	−18.6775	−0.736567	−0.368284	+	0.929713i	$0.620054\pi$
$644$	1.22079	0.0481060
$645$	100.401	3.95328
$646$	0	0
$647$	6.27089	0.246534	0.123267	−	0.992374i	$-0.460663\pi$
$647$	6.27089	0.246534	0.123267	+	0.992374i	$0.460663\pi$
$648$	−10.1068	−0.397033
$649$	1.53229	0.0601478
$650$	−64.8744	−2.54458
$651$	−5.70301	−0.223518
$652$	−3.25499	−0.127475
$653$	4.02033	0.157328	0.0786639	−	0.996901i	$-0.474935\pi$
$653$	4.02033	0.157328	0.0786639	+	0.996901i	$0.474935\pi$
$654$	11.8717	0.464220
$655$	93.0108	3.63423
$656$	1.69201	0.0660617
$657$	33.3086	1.29949
$658$	−10.7789	−0.420206
$659$	31.6704	1.23370	0.616852	−	0.787079i	$-0.288408\pi$
$659$	31.6704	1.23370	0.616852	+	0.787079i	$0.288408\pi$
$660$	19.6787	0.765991
$661$	3.62931	0.141164	0.0705818	−	0.997506i	$-0.477514\pi$
$661$	3.62931	0.141164	0.0705818	+	0.997506i	$0.477514\pi$
$662$	−11.2710	−0.438062
$663$	−77.8185	−3.02222
$664$	−5.55170	−0.215448
$665$	0	0
$666$	−21.9976	−0.852391
$667$	−4.13057	−0.159936
$668$	−1.99367	−0.0771375
$669$	26.0239	1.00614
$670$	−24.0918	−0.930748
$671$	3.56814	0.137747
$672$	2.35992	0.0910357
$673$	−27.4250	−1.05715	−0.528577	−	0.848885i	$-0.677274\pi$
$673$	−27.4250	−1.05715	−0.528577	+	0.848885i	$0.677274\pi$
$674$	14.3044	0.550986
$675$	−12.0120	−0.462343
$676$	17.1475	0.659519
$677$	−7.71944	−0.296682	−0.148341	−	0.988936i	$-0.547393\pi$
$677$	−7.71944	−0.296682	−0.148341	+	0.988936i	$0.547393\pi$
$678$	−32.9971	−1.26725
$679$	9.13311	0.350497
$680$	−24.6272	−0.944408
$681$	32.1095	1.23044
$682$	4.91420	0.188174
$683$	−11.7558	−0.449822	−0.224911	−	0.974379i	$-0.572209\pi$
$683$	−11.7558	−0.449822	−0.224911	+	0.974379i	$0.572209\pi$
$684$	0	0
$685$	−20.1187	−0.768696
$686$	1.00000	0.0381802
$687$	−44.3291	−1.69126
$688$	−10.3750	−0.395542
$689$	50.5310	1.92508
$690$	−11.8139	−0.449746
$691$	−39.0536	−1.48567	−0.742835	−	0.669474i	$-0.766519\pi$
$691$	−39.0536	−1.48567	−0.742835	+	0.669474i	$0.766519\pi$
$692$	23.5491	0.895203
$693$	−5.22449	−0.198462
$694$	−5.22077	−0.198178
$695$	70.7052	2.68200
$696$	−7.98482	−0.302664
$697$	10.1616	0.384899
$698$	15.4070	0.583164
$699$	3.05412	0.115518
$700$	11.8154	0.446580
$701$	36.0755	1.36255	0.681277	−	0.732026i	$-0.261425\pi$
$701$	36.0755	1.36255	0.681277	+	0.732026i	$0.261425\pi$
$702$	5.58205	0.210681
$703$	0	0
$704$	−2.03351	−0.0766407
$705$	104.310	3.92853
$706$	2.37291	0.0893057
$707$	9.18698	0.345512
$708$	−1.77825	−0.0668308
$709$	−25.5943	−0.961215	−0.480608	−	0.876936i	$-0.659584\pi$
$709$	−25.5943	−0.961215	−0.480608	+	0.876936i	$0.659584\pi$
$710$	16.9050	0.634433
$711$	−32.4813	−1.21814
$712$	15.6749	0.587443
$713$	−2.95019	−0.110485
$714$	14.1729	0.530406
$715$	−45.7852	−1.71227
$716$	−1.78906	−0.0668604
$717$	2.09900	0.0783887
$718$	10.3620	0.386705
$719$	−38.0418	−1.41872	−0.709359	−	0.704847i	$-0.751016\pi$
$719$	−38.0418	−1.41872	−0.709359	+	0.704847i	$0.751016\pi$
$720$	−10.5354	−0.392632
$721$	−9.89474	−0.368499
$722$	0	0
$723$	−69.3286	−2.57836
$724$	1.95922	0.0728138
$725$	−39.9776	−1.48473
$726$	−16.2005	−0.601256
$727$	−3.88188	−0.143971	−0.0719856	−	0.997406i	$-0.522934\pi$
$727$	−3.88188	−0.143971	−0.0719856	+	0.997406i	$0.522934\pi$
$728$	−5.49067	−0.203498
$729$	−18.7689	−0.695143
$730$	−53.1633	−1.96766
$731$	−62.3086	−2.30457
$732$	−4.14088	−0.153051
$733$	19.9843	0.738138	0.369069	−	0.929402i	$-0.379677\pi$
$733$	19.9843	0.738138	0.369069	+	0.929402i	$0.379677\pi$
$734$	−19.9753	−0.737300
$735$	−9.67721	−0.356949
$736$	1.22079	0.0449990
$737$	−11.9471	−0.440076
$738$	4.34711	0.160019
$739$	−35.2735	−1.29756	−0.648779	−	0.760977i	$-0.724720\pi$
$739$	−35.2735	−1.29756	−0.648779	+	0.760977i	$0.724720\pi$
$740$	35.1100	1.29067
$741$	0	0
$742$	−9.20307	−0.337855
$743$	12.5635	0.460911	0.230455	−	0.973083i	$-0.425978\pi$
$743$	12.5635	0.460911	0.230455	+	0.973083i	$0.425978\pi$
$744$	−5.70301	−0.209082
$745$	−77.7158	−2.84729
$746$	6.59897	0.241605
$747$	−14.2635	−0.521873
$748$	−12.2126	−0.446535
$749$	−2.46875	−0.0902061
$750$	−65.9539	−2.40830
$751$	−2.61750	−0.0955139	−0.0477569	−	0.998859i	$-0.515207\pi$
$751$	−2.61750	−0.0955139	−0.0477569	+	0.998859i	$0.515207\pi$
$752$	−10.7789	−0.393067
$753$	67.9005	2.47443
$754$	18.5778	0.676563
$755$	16.8111	0.611820
$756$	−1.01664	−0.0369749
$757$	−17.8523	−0.648852	−0.324426	−	0.945911i	$-0.605171\pi$
$757$	−17.8523	−0.648852	−0.324426	+	0.945911i	$0.605171\pi$
$758$	−31.9921	−1.16201
$759$	−5.85847	−0.212649
$760$	0	0
$761$	−9.67589	−0.350751	−0.175375	−	0.984502i	$-0.556114\pi$
$761$	−9.67589	−0.350751	−0.175375	+	0.984502i	$0.556114\pi$
$762$	−41.1598	−1.49106
$763$	5.03056	0.182119
$764$	0.753847	0.0272732
$765$	−63.2722	−2.28761
$766$	−0.351820	−0.0127118
$767$	4.13735	0.149391
$768$	2.35992	0.0851561
$769$	30.5348	1.10111	0.550557	−	0.834797i	$-0.314415\pi$
$769$	30.5348	1.10111	0.550557	+	0.834797i	$0.314415\pi$
$770$	8.33871	0.300506
$771$	30.2917	1.09093
$772$	6.31071	0.227127
$773$	43.9507	1.58080	0.790399	−	0.612592i	$-0.209873\pi$
$773$	43.9507	1.58080	0.790399	+	0.612592i	$0.209873\pi$
$774$	−26.6554	−0.958110
$775$	−28.5532	−1.02566
$776$	9.13311	0.327860
$777$	−20.2057	−0.724875
$778$	−19.8365	−0.711174
$779$	0	0
$780$	53.1344	1.90252
$781$	8.38315	0.299973
$782$	7.33167	0.262180
$783$	3.43983	0.122929
$784$	1.00000	0.0357143
$785$	−46.3543	−1.65445
$786$	−53.5274	−1.90926
$787$	40.2776	1.43574	0.717870	−	0.696177i	$-0.245117\pi$
$787$	40.2776	1.43574	0.717870	+	0.696177i	$0.245117\pi$
$788$	−11.7879	−0.419926
$789$	35.4499	1.26205
$790$	51.8428	1.84448
$791$	−13.9823	−0.497154
$792$	−5.22449	−0.185644
$793$	9.63434	0.342126
$794$	18.6253	0.660986
$795$	89.0600	3.15863
$796$	16.2045	0.574354
$797$	5.55040	0.196605	0.0983026	−	0.995157i	$-0.468659\pi$
$797$	5.55040	0.196605	0.0983026	+	0.995157i	$0.468659\pi$
$798$	0	0
$799$	−64.7345	−2.29014
$800$	11.8154	0.417737
$801$	40.2721	1.42295
$802$	−15.2434	−0.538262
$803$	−26.3636	−0.930350
$804$	13.8648	0.488973
$805$	−5.00605	−0.176440
$806$	13.2688	0.467375
$807$	−12.7675	−0.449438
$808$	9.18698	0.323197
$809$	45.7888	1.60985	0.804925	−	0.593377i	$-0.202206\pi$
$809$	45.7888	1.60985	0.804925	+	0.593377i	$0.202206\pi$
$810$	41.4445	1.45621
$811$	−13.6655	−0.479862	−0.239931	−	0.970790i	$-0.577125\pi$
$811$	−13.6655	−0.479862	−0.239931	+	0.970790i	$0.577125\pi$
$812$	−3.38352	−0.118738
$813$	46.1578	1.61883
$814$	17.4110	0.610254
$815$	13.3476	0.467546
$816$	14.1729	0.496149
$817$	0	0
$818$	−10.7468	−0.375751
$819$	−14.1067	−0.492927
$820$	−6.93834	−0.242297
$821$	22.3759	0.780923	0.390462	−	0.920619i	$-0.372315\pi$
$821$	22.3759	0.780923	0.390462	+	0.920619i	$0.372315\pi$
$822$	11.5783	0.403838
$823$	−9.04169	−0.315173	−0.157587	−	0.987505i	$-0.550371\pi$
$823$	−9.04169	−0.315173	−0.157587	+	0.987505i	$0.550371\pi$
$824$	−9.89474	−0.344700
$825$	−56.7009	−1.97407
$826$	−0.753523	−0.0262184
$827$	19.2711	0.670122	0.335061	−	0.942196i	$-0.391243\pi$
$827$	19.2711	0.670122	0.335061	+	0.942196i	$0.391243\pi$
$828$	3.13647	0.109000
$829$	−10.7222	−0.372396	−0.186198	−	0.982512i	$-0.559617\pi$
$829$	−10.7222	−0.372396	−0.186198	+	0.982512i	$0.559617\pi$
$830$	22.7656	0.790207
$831$	40.4148	1.40197
$832$	−5.49067	−0.190355
$833$	6.00566	0.208084
$834$	−40.6906	−1.40900
$835$	8.17537	0.282920
$836$	0	0
$837$	2.45683	0.0849206
$838$	30.5702	1.05603
$839$	3.32518	0.114798	0.0573991	−	0.998351i	$-0.481719\pi$
$839$	3.32518	0.114798	0.0573991	+	0.998351i	$0.481719\pi$
$840$	−9.67721	−0.333895
$841$	−17.5518	−0.605235
$842$	16.7182	0.576147
$843$	−35.2084	−1.21264
$844$	−8.28584	−0.285210
$845$	−70.3160	−2.41894
$846$	−27.6932	−0.952113
$847$	−6.86485	−0.235879
$848$	−9.20307	−0.316035
$849$	−31.9973	−1.09815
$850$	70.9592	2.43388
$851$	−10.4525	−0.358306
$852$	−9.72877	−0.333302
$853$	11.7950	0.403855	0.201927	−	0.979401i	$-0.435280\pi$
$853$	11.7950	0.403855	0.201927	+	0.979401i	$0.435280\pi$
$854$	−1.75467	−0.0600437
$855$	0	0
$856$	−2.46875	−0.0843801
$857$	12.6094	0.430728	0.215364	−	0.976534i	$-0.430906\pi$
$857$	12.6094	0.430728	0.215364	+	0.976534i	$0.430906\pi$
$858$	26.3492	0.899548
$859$	−38.3227	−1.30755	−0.653777	−	0.756687i	$-0.726816\pi$
$859$	−38.3227	−1.30755	−0.653777	+	0.756687i	$0.726816\pi$
$860$	42.5442	1.45075
$861$	3.99299	0.136081
$862$	32.7077	1.11403
$863$	17.7945	0.605733	0.302866	−	0.953033i	$-0.402056\pi$
$863$	17.7945	0.605733	0.302866	+	0.953033i	$0.402056\pi$
$864$	−1.01664	−0.0345869
$865$	−96.5668	−3.28337
$866$	−4.86618	−0.165359
$867$	44.9988	1.52824
$868$	−2.41661	−0.0820252
$869$	25.7087	0.872108
$870$	32.7430	1.11009
$871$	−32.2583	−1.09303
$872$	5.03056	0.170356
$873$	23.4648	0.794164
$874$	0	0
$875$	−27.9476	−0.944800
$876$	30.5953	1.03372
$877$	−40.6605	−1.37301	−0.686504	−	0.727126i	$-0.740856\pi$
$877$	−40.6605	−1.37301	−0.686504	+	0.727126i	$0.740856\pi$
$878$	6.27304	0.211705
$879$	16.8823	0.569426
$880$	8.33871	0.281098
$881$	7.47678	0.251899	0.125950	−	0.992037i	$-0.459802\pi$
$881$	7.47678	0.251899	0.125950	+	0.992037i	$0.459802\pi$
$882$	2.56920	0.0865096
$883$	27.9077	0.939168	0.469584	−	0.882888i	$-0.344404\pi$
$883$	27.9077	0.939168	0.469584	+	0.882888i	$0.344404\pi$
$884$	−32.9751	−1.10907
$885$	7.29200	0.245118
$886$	−1.73179	−0.0581805
$887$	−43.3242	−1.45469	−0.727343	−	0.686274i	$-0.759245\pi$
$887$	−43.3242	−1.45469	−0.727343	+	0.686274i	$0.759245\pi$
$888$	−20.2057	−0.678059
$889$	−17.4412	−0.584959
$890$	−64.2776	−2.15459
$891$	20.5523	0.688526
$892$	11.0275	0.369228
$893$	0	0
$894$	44.7252	1.49583
$895$	7.33633	0.245227
$896$	1.00000	0.0334077
$897$	−15.8185	−0.528163
$898$	4.58054	0.152855
$899$	8.17665	0.272707
$900$	30.3561	1.01187
$901$	−55.2705	−1.84133
$902$	−3.44071	−0.114563
$903$	−24.4841	−0.814779
$904$	−13.9823	−0.465045
$905$	−8.03408	−0.267062
$906$	−9.67477	−0.321423
$907$	31.9818	1.06194	0.530969	−	0.847391i	$-0.321828\pi$
$907$	31.9818	1.06194	0.530969	+	0.847391i	$0.321828\pi$
$908$	13.6062	0.451537
$909$	23.6032	0.782869
$910$	22.5154	0.746377
$911$	−8.42748	−0.279215	−0.139607	−	0.990207i	$-0.544584\pi$
$911$	−8.42748	−0.279215	−0.139607	+	0.990207i	$0.544584\pi$
$912$	0	0
$913$	11.2894	0.373626
$914$	9.34917	0.309243
$915$	16.9803	0.561353
$916$	−18.7842	−0.620647
$917$	−22.6819	−0.749023
$918$	−6.10561	−0.201515
$919$	17.5956	0.580426	0.290213	−	0.956962i	$-0.406274\pi$
$919$	17.5956	0.580426	0.290213	+	0.956962i	$0.406274\pi$
$920$	−5.00605	−0.165045
$921$	77.9679	2.56913
$922$	12.6825	0.417675
$923$	22.6353	0.745051
$924$	−4.79891	−0.157872
$925$	−101.164	−3.32625
$926$	−12.8438	−0.422073
$927$	−25.4216	−0.834955
$928$	−3.38352	−0.111069
$929$	49.2072	1.61444	0.807218	−	0.590254i	$-0.200972\pi$
$929$	49.2072	1.61444	0.807218	+	0.590254i	$0.200972\pi$
$930$	23.3861	0.766860
$931$	0	0
$932$	1.29417	0.0423918
$933$	2.76516	0.0905272
$934$	−17.4065	−0.569560
$935$	50.0795	1.63777
$936$	−14.1067	−0.461091
$937$	−57.1571	−1.86724	−0.933620	−	0.358264i	$-0.883369\pi$
$937$	−57.1571	−1.86724	−0.933620	+	0.358264i	$0.883369\pi$
$938$	5.87511	0.191829
$939$	−15.7252	−0.513174
$940$	44.2006	1.44167
$941$	−54.5718	−1.77899	−0.889495	−	0.456946i	$-0.848943\pi$
$941$	−54.5718	−1.77899	−0.889495	+	0.456946i	$0.848943\pi$
$942$	26.6767	0.869175
$943$	2.06559	0.0672648
$944$	−0.753523	−0.0245251
$945$	4.16890	0.135614
$946$	21.0976	0.685942
$947$	24.6518	0.801075	0.400537	−	0.916280i	$-0.368823\pi$
$947$	24.6518	0.801075	0.400537	+	0.916280i	$0.368823\pi$
$948$	−29.8354	−0.969007
$949$	−71.1843	−2.31074
$950$	0	0
$951$	25.9402	0.841168
$952$	6.00566	0.194645
$953$	−25.8202	−0.836398	−0.418199	−	0.908355i	$-0.637339\pi$
$953$	−25.8202	−0.836398	−0.418199	+	0.908355i	$0.637339\pi$
$954$	−23.6446	−0.765521
$955$	−3.09127	−0.100031
$956$	0.889440	0.0287665
$957$	16.2372	0.524873
$958$	−15.5581	−0.502660
$959$	4.90621	0.158430
$960$	−9.67721	−0.312330
$961$	−25.1600	−0.811612
$962$	47.0114	1.51571
$963$	−6.34272	−0.204391
$964$	−29.3776	−0.946188
$965$	−25.8781	−0.833044
$966$	2.88097	0.0926937
$967$	−1.73509	−0.0557966	−0.0278983	−	0.999611i	$-0.508881\pi$
$967$	−1.73509	−0.0557966	−0.0278983	+	0.999611i	$0.508881\pi$
$968$	−6.86485	−0.220645
$969$	0	0
$970$	−37.4518	−1.20250
$971$	37.9621	1.21826	0.609131	−	0.793070i	$-0.291518\pi$
$971$	37.9621	1.21826	0.609131	+	0.793070i	$0.291518\pi$
$972$	−20.8013	−0.667201
$973$	−17.2424	−0.552766
$974$	−2.88504	−0.0924427
$975$	−153.098	−4.90307
$976$	−1.75467	−0.0561658
$977$	−1.77259	−0.0567101	−0.0283550	−	0.999598i	$-0.509027\pi$
$977$	−1.77259	−0.0567101	−0.0283550	+	0.999598i	$0.509027\pi$
$978$	−7.68150	−0.245627
$979$	−31.8751	−1.01873
$980$	−4.10066	−0.130991
$981$	12.9245	0.412649
$982$	7.75242	0.247390
$983$	−45.0465	−1.43676	−0.718379	−	0.695651i	$-0.755116\pi$
$983$	−45.0465	−1.43676	−0.718379	+	0.695651i	$0.755116\pi$
$984$	3.99299	0.127292
$985$	48.3381	1.54018
$986$	−20.3203	−0.647129
$987$	−25.4373	−0.809679
$988$	0	0
$989$	−12.6657	−0.402746
$990$	21.4239	0.680895
$991$	−11.6186	−0.369076	−0.184538	−	0.982825i	$-0.559079\pi$
$991$	−11.6186	−0.369076	−0.184538	+	0.982825i	$0.559079\pi$
$992$	−2.41661	−0.0767276
$993$	−26.5987	−0.844085
$994$	−4.12251	−0.130758
$995$	−66.4492	−2.10658
$996$	−13.1016	−0.415139
$997$	11.4729	0.363349	0.181675	−	0.983359i	$-0.441848\pi$
$997$	11.4729	0.363349	0.181675	+	0.983359i	$0.441848\pi$
$998$	29.5766	0.936230
$999$	8.70454	0.275399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bh.1.8	yes	8
19.18	odd	2		5054.2.a.bg.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.bg.1.1	✓	8	19.18	odd	2
5054.2.a.bh.1.8	yes	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.35992 q^{3} +1.00000 q^{4} -4.10066 q^{5} +2.35992 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.56920 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.35992 q^{3} +1.00000 q^{4} -4.10066 q^{5} +2.35992 q^{6} +1.00000 q^{7} +1.00000 q^{8} +2.56920 q^{9} -4.10066 q^{10} -2.03351 q^{11} +2.35992 q^{12} -5.49067 q^{13} +1.00000 q^{14} -9.67721 q^{15} +1.00000 q^{16} +6.00566 q^{17} +2.56920 q^{18} -4.10066 q^{20} +2.35992 q^{21} -2.03351 q^{22} +1.22079 q^{23} +2.35992 q^{24} +11.8154 q^{25} -5.49067 q^{26} -1.01664 q^{27} +1.00000 q^{28} -3.38352 q^{29} -9.67721 q^{30} -2.41661 q^{31} +1.00000 q^{32} -4.79891 q^{33} +6.00566 q^{34} -4.10066 q^{35} +2.56920 q^{36} -8.56204 q^{37} -12.9575 q^{39} -4.10066 q^{40} +1.69201 q^{41} +2.35992 q^{42} -10.3750 q^{43} -2.03351 q^{44} -10.5354 q^{45} +1.22079 q^{46} -10.7789 q^{47} +2.35992 q^{48} +1.00000 q^{49} +11.8154 q^{50} +14.1729 q^{51} -5.49067 q^{52} -9.20307 q^{53} -1.01664 q^{54} +8.33871 q^{55} +1.00000 q^{56} -3.38352 q^{58} -0.753523 q^{59} -9.67721 q^{60} -1.75467 q^{61} -2.41661 q^{62} +2.56920 q^{63} +1.00000 q^{64} +22.5154 q^{65} -4.79891 q^{66} +5.87511 q^{67} +6.00566 q^{68} +2.88097 q^{69} -4.10066 q^{70} -4.12251 q^{71} +2.56920 q^{72} +12.9646 q^{73} -8.56204 q^{74} +27.8833 q^{75} -2.03351 q^{77} -12.9575 q^{78} -12.6425 q^{79} -4.10066 q^{80} -10.1068 q^{81} +1.69201 q^{82} -5.55170 q^{83} +2.35992 q^{84} -24.6272 q^{85} -10.3750 q^{86} -7.98482 q^{87} -2.03351 q^{88} +15.6749 q^{89} -10.5354 q^{90} -5.49067 q^{91} +1.22079 q^{92} -5.70301 q^{93} -10.7789 q^{94} +2.35992 q^{96} +9.13311 q^{97} +1.00000 q^{98} -5.22449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9} - 2 q^{10} - 12 q^{11} - 4 q^{12} - 10 q^{13} + 8 q^{14} - 24 q^{15} + 8 q^{16} - 6 q^{17} + 8 q^{18} - 2 q^{20} - 4 q^{21} - 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} - 22 q^{27} + 8 q^{28} - 8 q^{29} - 24 q^{30} - 18 q^{31} + 8 q^{32} + 16 q^{33} - 6 q^{34} - 2 q^{35} + 8 q^{36} - 36 q^{37} - 2 q^{40} - 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} - 20 q^{46} - 10 q^{47} - 4 q^{48} + 8 q^{49} + 8 q^{50} - 12 q^{51} - 10 q^{52} - 32 q^{53} - 22 q^{54} - 22 q^{55} + 8 q^{56} - 8 q^{58} + 2 q^{59} - 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} - 44 q^{67} - 6 q^{68} - 2 q^{70} - 8 q^{71} + 8 q^{72} + 30 q^{73} - 36 q^{74} + 16 q^{75} - 12 q^{77} - 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} - 4 q^{84} - 16 q^{85} - 16 q^{86} + 24 q^{87} - 12 q^{88} + 22 q^{89} + 8 q^{90} - 10 q^{91} - 20 q^{92} - 16 q^{93} - 10 q^{94} - 4 q^{96} + 6 q^{97} + 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 + 8 * q^8 + 8 * q^9 - 2 * q^10 - 12 * q^11 - 4 * q^12 - 10 * q^13 + 8 * q^14 - 24 * q^15 + 8 * q^16 - 6 * q^17 + 8 * q^18 - 2 * q^20 - 4 * q^21 - 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 - 22 * q^27 + 8 * q^28 - 8 * q^29 - 24 * q^30 - 18 * q^31 + 8 * q^32 + 16 * q^33 - 6 * q^34 - 2 * q^35 + 8 * q^36 - 36 * q^37 - 2 * q^40 - 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 - 20 * q^46 - 10 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 - 12 * q^51 - 10 * q^52 - 32 * q^53 - 22 * q^54 - 22 * q^55 + 8 * q^56 - 8 * q^58 + 2 * q^59 - 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 - 44 * q^67 - 6 * q^68 - 2 * q^70 - 8 * q^71 + 8 * q^72 + 30 * q^73 - 36 * q^74 + 16 * q^75 - 12 * q^77 - 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 - 4 * q^84 - 16 * q^85 - 16 * q^86 + 24 * q^87 - 12 * q^88 + 22 * q^89 + 8 * q^90 - 10 * q^91 - 20 * q^92 - 16 * q^93 - 10 * q^94 - 4 * q^96 + 6 * q^97 + 8 * q^98 - 52 * q^99

Introduction

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