LMFDB - Embedded newform 5054.2.a.bi.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:	$8$
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			1.7
Root			$2.04552$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.40760 q^{3} +1.00000 q^{4} +1.76144 q^{5} +2.40760 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.79656 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.40760 q^{3} +1.00000 q^{4} +1.76144 q^{5} +2.40760 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.79656 q^{9} +1.76144 q^{10} +1.18414 q^{11} +2.40760 q^{12} +0.361568 q^{13} -1.00000 q^{14} +4.24085 q^{15} +1.00000 q^{16} +3.54532 q^{17} +2.79656 q^{18} +1.76144 q^{20} -2.40760 q^{21} +1.18414 q^{22} -2.87691 q^{23} +2.40760 q^{24} -1.89733 q^{25} +0.361568 q^{26} -0.489807 q^{27} -1.00000 q^{28} +5.10308 q^{29} +4.24085 q^{30} -1.38152 q^{31} +1.00000 q^{32} +2.85095 q^{33} +3.54532 q^{34} -1.76144 q^{35} +2.79656 q^{36} -3.35526 q^{37} +0.870512 q^{39} +1.76144 q^{40} +10.0120 q^{41} -2.40760 q^{42} +3.47246 q^{43} +1.18414 q^{44} +4.92597 q^{45} -2.87691 q^{46} +11.6169 q^{47} +2.40760 q^{48} +1.00000 q^{49} -1.89733 q^{50} +8.53574 q^{51} +0.361568 q^{52} +12.0168 q^{53} -0.489807 q^{54} +2.08580 q^{55} -1.00000 q^{56} +5.10308 q^{58} -7.72735 q^{59} +4.24085 q^{60} -1.99042 q^{61} -1.38152 q^{62} -2.79656 q^{63} +1.00000 q^{64} +0.636880 q^{65} +2.85095 q^{66} +8.30406 q^{67} +3.54532 q^{68} -6.92645 q^{69} -1.76144 q^{70} -0.226733 q^{71} +2.79656 q^{72} -14.0163 q^{73} -3.35526 q^{74} -4.56803 q^{75} -1.18414 q^{77} +0.870512 q^{78} +5.28063 q^{79} +1.76144 q^{80} -9.56894 q^{81} +10.0120 q^{82} +13.3912 q^{83} -2.40760 q^{84} +6.24487 q^{85} +3.47246 q^{86} +12.2862 q^{87} +1.18414 q^{88} -1.87916 q^{89} +4.92597 q^{90} -0.361568 q^{91} -2.87691 q^{92} -3.32616 q^{93} +11.6169 q^{94} +2.40760 q^{96} -3.99766 q^{97} +1.00000 q^{98} +3.31153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 6 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 + 6 * q^5 + 4 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{10} + 4 q^{11} + 4 q^{12} + 6 q^{13} - 8 q^{14} + 8 q^{15} + 8 q^{16} + 2 q^{17} + 8 q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{22} + 20 q^{23} + 4 q^{24} - 8 q^{25} + 6 q^{26} + 22 q^{27} - 8 q^{28} + 16 q^{29} + 8 q^{30} + 22 q^{31} + 8 q^{32} - 8 q^{33} + 2 q^{34} - 6 q^{35} + 8 q^{36} - 12 q^{37} + 8 q^{39} + 6 q^{40} + 36 q^{41} - 4 q^{42} + 4 q^{44} - 4 q^{45} + 20 q^{46} + 6 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} - 4 q^{51} + 6 q^{52} + 16 q^{53} + 22 q^{54} + 18 q^{55} - 8 q^{56} + 16 q^{58} + 14 q^{59} + 8 q^{60} + 10 q^{61} + 22 q^{62} - 8 q^{63} + 8 q^{64} + 32 q^{65} - 8 q^{66} - 20 q^{67} + 2 q^{68} + 40 q^{69} - 6 q^{70} + 8 q^{72} - 18 q^{73} - 12 q^{74} + 16 q^{75} - 4 q^{77} + 8 q^{78} + 4 q^{79} + 6 q^{80} + 12 q^{81} + 36 q^{82} + 36 q^{83} - 4 q^{84} - 16 q^{85} + 28 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{90} - 6 q^{91} + 20 q^{92} + 16 q^{93} + 6 q^{94} + 4 q^{96} + 26 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^10 + 4 * q^11 + 4 * q^12 + 6 * q^13 - 8 * q^14 + 8 * q^15 + 8 * q^16 + 2 * q^17 + 8 * q^18 + 6 * q^20 - 4 * q^21 + 4 * q^22 + 20 * q^23 + 4 * q^24 - 8 * q^25 + 6 * q^26 + 22 * q^27 - 8 * q^28 + 16 * q^29 + 8 * q^30 + 22 * q^31 + 8 * q^32 - 8 * q^33 + 2 * q^34 - 6 * q^35 + 8 * q^36 - 12 * q^37 + 8 * q^39 + 6 * q^40 + 36 * q^41 - 4 * q^42 + 4 * q^44 - 4 * q^45 + 20 * q^46 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 - 4 * q^51 + 6 * q^52 + 16 * q^53 + 22 * q^54 + 18 * q^55 - 8 * q^56 + 16 * q^58 + 14 * q^59 + 8 * q^60 + 10 * q^61 + 22 * q^62 - 8 * q^63 + 8 * q^64 + 32 * q^65 - 8 * q^66 - 20 * q^67 + 2 * q^68 + 40 * q^69 - 6 * q^70 + 8 * q^72 - 18 * q^73 - 12 * q^74 + 16 * q^75 - 4 * q^77 + 8 * q^78 + 4 * q^79 + 6 * q^80 + 12 * q^81 + 36 * q^82 + 36 * q^83 - 4 * q^84 - 16 * q^85 + 28 * q^87 + 4 * q^88 + 18 * q^89 - 4 * q^90 - 6 * q^91 + 20 * q^92 + 16 * q^93 + 6 * q^94 + 4 * q^96 + 26 * q^97 + 8 * q^98 + 4 * 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
$3$	2.40760	1.39003	0.695015	−	0.718995i	$-0.255397\pi$
$3$	2.40760	1.39003	0.695015	+	0.718995i	$0.255397\pi$
$4$	1.00000	0.500000
$5$	1.76144	0.787739	0.393870	−	0.919166i	$-0.371136\pi$
$5$	1.76144	0.787739	0.393870	+	0.919166i	$0.371136\pi$
$6$	2.40760	0.982900
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	2.79656	0.932186
$10$	1.76144	0.557016
$11$	1.18414	0.357033	0.178516	−	0.983937i	$-0.442870\pi$
$11$	1.18414	0.357033	0.178516	+	0.983937i	$0.442870\pi$
$12$	2.40760	0.695015
$13$	0.361568	0.100281	0.0501404	−	0.998742i	$-0.484033\pi$
$13$	0.361568	0.100281	0.0501404	+	0.998742i	$0.484033\pi$
$14$	−1.00000	−0.267261
$15$	4.24085	1.09498
$16$	1.00000	0.250000
$17$	3.54532	0.859868	0.429934	−	0.902860i	$-0.358537\pi$
$17$	3.54532	0.859868	0.429934	+	0.902860i	$0.358537\pi$
$18$	2.79656	0.659155
$19$	0	0
$19$	0	0
$20$	1.76144	0.393870
$21$	−2.40760	−0.525382
$22$	1.18414	0.252460
$23$	−2.87691	−0.599877	−0.299938	−	0.953959i	$-0.596966\pi$
$23$	−2.87691	−0.599877	−0.299938	+	0.953959i	$0.596966\pi$
$24$	2.40760	0.491450
$25$	−1.89733	−0.379467
$26$	0.361568	0.0709093
$27$	−0.489807	−0.0942634
$28$	−1.00000	−0.188982
$29$	5.10308	0.947618	0.473809	−	0.880628i	$-0.342879\pi$
$29$	5.10308	0.947618	0.473809	+	0.880628i	$0.342879\pi$
$30$	4.24085	0.774269
$31$	−1.38152	−0.248129	−0.124064	−	0.992274i	$-0.539593\pi$
$31$	−1.38152	−0.248129	−0.124064	+	0.992274i	$0.539593\pi$
$32$	1.00000	0.176777
$33$	2.85095	0.496286
$34$	3.54532	0.608018
$35$	−1.76144	−0.297737
$36$	2.79656	0.466093
$37$	−3.35526	−0.551602	−0.275801	−	0.961215i	$-0.588943\pi$
$37$	−3.35526	−0.551602	−0.275801	+	0.961215i	$0.588943\pi$
$38$	0	0
$39$	0.870512	0.139394
$40$	1.76144	0.278508
$41$	10.0120	1.56361	0.781803	−	0.623526i	$-0.214300\pi$
$41$	10.0120	1.56361	0.781803	+	0.623526i	$0.214300\pi$
$42$	−2.40760	−0.371501
$43$	3.47246	0.529545	0.264772	−	0.964311i	$-0.414703\pi$
$43$	3.47246	0.529545	0.264772	+	0.964311i	$0.414703\pi$
$44$	1.18414	0.178516
$45$	4.92597	0.734320
$46$	−2.87691	−0.424177
$47$	11.6169	1.69451	0.847253	−	0.531190i	$-0.178255\pi$
$47$	11.6169	1.69451	0.847253	+	0.531190i	$0.178255\pi$
$48$	2.40760	0.347508
$49$	1.00000	0.142857
$50$	−1.89733	−0.268323
$51$	8.53574	1.19524
$52$	0.361568	0.0501404
$53$	12.0168	1.65063	0.825316	−	0.564672i	$-0.190997\pi$
$53$	12.0168	1.65063	0.825316	+	0.564672i	$0.190997\pi$
$54$	−0.489807	−0.0666543
$55$	2.08580	0.281249
$56$	−1.00000	−0.133631
$57$	0	0
$58$	5.10308	0.670067
$59$	−7.72735	−1.00602	−0.503008	−	0.864282i	$-0.667773\pi$
$59$	−7.72735	−1.00602	−0.503008	+	0.864282i	$0.667773\pi$
$60$	4.24085	0.547491
$61$	−1.99042	−0.254848	−0.127424	−	0.991848i	$-0.540671\pi$
$61$	−1.99042	−0.254848	−0.127424	+	0.991848i	$0.540671\pi$
$62$	−1.38152	−0.175453
$63$	−2.79656	−0.352333
$64$	1.00000	0.125000
$65$	0.636880	0.0789952
$66$	2.85095	0.350927
$67$	8.30406	1.01450	0.507251	−	0.861798i	$-0.330662\pi$
$67$	8.30406	1.01450	0.507251	+	0.861798i	$0.330662\pi$
$68$	3.54532	0.429934
$69$	−6.92645	−0.833847
$70$	−1.76144	−0.210532
$71$	−0.226733	−0.0269083	−0.0134541	−	0.999909i	$-0.504283\pi$
$71$	−0.226733	−0.0269083	−0.0134541	+	0.999909i	$0.504283\pi$
$72$	2.79656	0.329578
$73$	−14.0163	−1.64048	−0.820242	−	0.572017i	$-0.806161\pi$
$73$	−14.0163	−1.64048	−0.820242	+	0.572017i	$0.806161\pi$
$74$	−3.35526	−0.390041
$75$	−4.56803	−0.527470
$76$	0	0
$77$	−1.18414	−0.134946
$78$	0.870512	0.0985661
$79$	5.28063	0.594118	0.297059	−	0.954859i	$-0.403994\pi$
$79$	5.28063	0.594118	0.297059	+	0.954859i	$0.403994\pi$
$80$	1.76144	0.196935
$81$	−9.56894	−1.06322
$82$	10.0120	1.10564
$83$	13.3912	1.46988	0.734939	−	0.678133i	$-0.237211\pi$
$83$	13.3912	1.46988	0.734939	+	0.678133i	$0.237211\pi$
$84$	−2.40760	−0.262691
$85$	6.24487	0.677351
$86$	3.47246	0.374445
$87$	12.2862	1.31722
$88$	1.18414	0.126230
$89$	−1.87916	−0.199191	−0.0995954	−	0.995028i	$-0.531755\pi$
$89$	−1.87916	−0.199191	−0.0995954	+	0.995028i	$0.531755\pi$
$90$	4.92597	0.519242
$91$	−0.361568	−0.0379026
$92$	−2.87691	−0.299938
$93$	−3.32616	−0.344906
$94$	11.6169	1.19820
$95$	0	0
$96$	2.40760	0.245725
$97$	−3.99766	−0.405901	−0.202950	−	0.979189i	$-0.565053\pi$
$97$	−3.99766	−0.405901	−0.202950	+	0.979189i	$0.565053\pi$
$98$	1.00000	0.101015
$99$	3.31153	0.332821
$100$	−1.89733	−0.189733
$101$	−18.6641	−1.85715	−0.928575	−	0.371145i	$-0.878965\pi$
$101$	−18.6641	−1.85715	−0.928575	+	0.371145i	$0.878965\pi$
$102$	8.53574	0.845164
$103$	−2.35245	−0.231793	−0.115897	−	0.993261i	$-0.536974\pi$
$103$	−2.35245	−0.231793	−0.115897	+	0.993261i	$0.536974\pi$
$104$	0.361568	0.0354546
$105$	−4.24085	−0.413864
$106$	12.0168	1.16717
$107$	−3.11852	−0.301479	−0.150739	−	0.988574i	$-0.548165\pi$
$107$	−3.11852	−0.301479	−0.150739	+	0.988574i	$0.548165\pi$
$108$	−0.489807	−0.0471317
$109$	−14.1835	−1.35853	−0.679266	−	0.733892i	$-0.737702\pi$
$109$	−14.1835	−1.35853	−0.679266	+	0.733892i	$0.737702\pi$
$110$	2.08580	0.198873
$111$	−8.07815	−0.766744
$112$	−1.00000	−0.0944911
$113$	−3.82085	−0.359436	−0.179718	−	0.983718i	$-0.557518\pi$
$113$	−3.82085	−0.359436	−0.179718	+	0.983718i	$0.557518\pi$
$114$	0	0
$115$	−5.06749	−0.472546
$116$	5.10308	0.473809
$117$	1.01115	0.0934804
$118$	−7.72735	−0.711360
$119$	−3.54532	−0.324999
$120$	4.24085	0.387135
$121$	−9.59781	−0.872528
$122$	−1.99042	−0.180205
$123$	24.1048	2.17346
$124$	−1.38152	−0.124064
$125$	−12.1492	−1.08666
$126$	−2.79656	−0.249137
$127$	−19.3815	−1.71983	−0.859917	−	0.510434i	$-0.829485\pi$
$127$	−19.3815	−1.71983	−0.859917	+	0.510434i	$0.829485\pi$
$128$	1.00000	0.0883883
$129$	8.36030	0.736084
$130$	0.636880	0.0558580
$131$	−4.99933	−0.436794	−0.218397	−	0.975860i	$-0.570083\pi$
$131$	−4.99933	−0.436794	−0.218397	+	0.975860i	$0.570083\pi$
$132$	2.85095	0.248143
$133$	0	0
$134$	8.30406	0.717362
$135$	−0.862765	−0.0742550
$136$	3.54532	0.304009
$137$	20.8876	1.78455	0.892276	−	0.451491i	$-0.149108\pi$
$137$	20.8876	1.78455	0.892276	+	0.451491i	$0.149108\pi$
$138$	−6.92645	−0.589619
$139$	−13.2393	−1.12294	−0.561472	−	0.827496i	$-0.689765\pi$
$139$	−13.2393	−1.12294	−0.561472	+	0.827496i	$0.689765\pi$
$140$	−1.76144	−0.148869
$141$	27.9690	2.35541
$142$	−0.226733	−0.0190270
$143$	0.428148	0.0358035
$144$	2.79656	0.233047
$145$	8.98876	0.746476
$146$	−14.0163	−1.16000
$147$	2.40760	0.198576
$148$	−3.35526	−0.275801
$149$	3.08216	0.252500	0.126250	−	0.991998i	$-0.459706\pi$
$149$	3.08216	0.252500	0.126250	+	0.991998i	$0.459706\pi$
$150$	−4.56803	−0.372978
$151$	−6.35364	−0.517052	−0.258526	−	0.966004i	$-0.583237\pi$
$151$	−6.35364	−0.517052	−0.258526	+	0.966004i	$0.583237\pi$
$152$	0	0
$153$	9.91471	0.801557
$154$	−1.18414	−0.0954210
$155$	−2.43347	−0.195461
$156$	0.870512	0.0696968
$157$	4.20918	0.335929	0.167965	−	0.985793i	$-0.446281\pi$
$157$	4.20918	0.335929	0.167965	+	0.985793i	$0.446281\pi$
$158$	5.28063	0.420105
$159$	28.9316	2.29443
$160$	1.76144	0.139254
$161$	2.87691	0.226732
$162$	−9.56894	−0.751807
$163$	7.15678	0.560562	0.280281	−	0.959918i	$-0.409572\pi$
$163$	7.15678	0.560562	0.280281	+	0.959918i	$0.409572\pi$
$164$	10.0120	0.781803
$165$	5.02177	0.390944
$166$	13.3912	1.03936
$167$	22.1964	1.71761	0.858806	−	0.512300i	$-0.171207\pi$
$167$	22.1964	1.71761	0.858806	+	0.512300i	$0.171207\pi$
$168$	−2.40760	−0.185751
$169$	−12.8693	−0.989944
$170$	6.24487	0.478960
$171$	0	0
$172$	3.47246	0.264772
$173$	10.8227	0.822835	0.411418	−	0.911447i	$-0.365034\pi$
$173$	10.8227	0.822835	0.411418	+	0.911447i	$0.365034\pi$
$174$	12.2862	0.931414
$175$	1.89733	0.143425
$176$	1.18414	0.0892581
$177$	−18.6044	−1.39839
$178$	−1.87916	−0.140849
$179$	−11.7586	−0.878880	−0.439440	−	0.898272i	$-0.644823\pi$
$179$	−11.7586	−0.878880	−0.439440	+	0.898272i	$0.644823\pi$
$180$	4.92597	0.367160
$181$	1.62634	0.120885	0.0604426	−	0.998172i	$-0.480749\pi$
$181$	1.62634	0.120885	0.0604426	+	0.998172i	$0.480749\pi$
$182$	−0.361568	−0.0268012
$183$	−4.79215	−0.354246
$184$	−2.87691	−0.212088
$185$	−5.91009	−0.434519
$186$	−3.32616	−0.243886
$187$	4.19817	0.307001
$188$	11.6169	0.847253
$189$	0.489807	0.0356282
$190$	0	0
$191$	15.1136	1.09358	0.546792	−	0.837268i	$-0.315849\pi$
$191$	15.1136	1.09358	0.546792	+	0.837268i	$0.315849\pi$
$192$	2.40760	0.173754
$193$	−21.0053	−1.51200	−0.755998	−	0.654574i	$-0.772848\pi$
$193$	−21.0053	−1.51200	−0.755998	+	0.654574i	$0.772848\pi$
$194$	−3.99766	−0.287015
$195$	1.53335	0.109806
$196$	1.00000	0.0714286
$197$	−24.5580	−1.74969	−0.874844	−	0.484405i	$-0.839036\pi$
$197$	−24.5580	−1.74969	−0.874844	+	0.484405i	$0.839036\pi$
$198$	3.31153	0.235340
$199$	5.50367	0.390145	0.195073	−	0.980789i	$-0.437506\pi$
$199$	5.50367	0.390145	0.195073	+	0.980789i	$0.437506\pi$
$200$	−1.89733	−0.134162
$201$	19.9929	1.41019
$202$	−18.6641	−1.31320
$203$	−5.10308	−0.358166
$204$	8.53574	0.597621
$205$	17.6355	1.23171
$206$	−2.35245	−0.163903
$207$	−8.04544	−0.559197
$208$	0.361568	0.0250702
$209$	0	0
$210$	−4.24085	−0.292646
$211$	4.53017	0.311870	0.155935	−	0.987767i	$-0.450161\pi$
$211$	4.53017	0.311870	0.155935	+	0.987767i	$0.450161\pi$
$212$	12.0168	0.825316
$213$	−0.545884	−0.0374033
$214$	−3.11852	−0.213178
$215$	6.11652	0.417143
$216$	−0.489807	−0.0333271
$217$	1.38152	0.0937838
$218$	−14.1835	−0.960628
$219$	−33.7457	−2.28032
$220$	2.08580	0.140624
$221$	1.28188	0.0862283
$222$	−8.07815	−0.542170
$223$	10.0211	0.671066	0.335533	−	0.942029i	$-0.391084\pi$
$223$	10.0211	0.671066	0.335533	+	0.942029i	$0.391084\pi$
$224$	−1.00000	−0.0668153
$225$	−5.30600	−0.353734
$226$	−3.82085	−0.254159
$227$	−7.43478	−0.493463	−0.246732	−	0.969084i	$-0.579357\pi$
$227$	−7.43478	−0.493463	−0.246732	+	0.969084i	$0.579357\pi$
$228$	0	0
$229$	3.96142	0.261778	0.130889	−	0.991397i	$-0.458217\pi$
$229$	3.96142	0.261778	0.130889	+	0.991397i	$0.458217\pi$
$230$	−5.06749	−0.334141
$231$	−2.85095	−0.187579
$232$	5.10308	0.335034
$233$	−14.3859	−0.942452	−0.471226	−	0.882012i	$-0.656188\pi$
$233$	−14.3859	−0.942452	−0.471226	+	0.882012i	$0.656188\pi$
$234$	1.01115	0.0661007
$235$	20.4625	1.33483
$236$	−7.72735	−0.503008
$237$	12.7137	0.825842
$238$	−3.54532	−0.229809
$239$	−7.12027	−0.460572	−0.230286	−	0.973123i	$-0.573966\pi$
$239$	−7.12027	−0.460572	−0.230286	+	0.973123i	$0.573966\pi$
$240$	4.24085	0.273746
$241$	−14.9816	−0.965051	−0.482525	−	0.875882i	$-0.660280\pi$
$241$	−14.9816	−0.965051	−0.482525	+	0.875882i	$0.660280\pi$
$242$	−9.59781	−0.616970
$243$	−21.5688	−1.38364
$244$	−1.99042	−0.127424
$245$	1.76144	0.112534
$246$	24.1048	1.53687
$247$	0	0
$248$	−1.38152	−0.0877267
$249$	32.2408	2.04318
$250$	−12.1492	−0.768385
$251$	−28.2614	−1.78385	−0.891923	−	0.452187i	$-0.850644\pi$
$251$	−28.2614	−1.78385	−0.891923	+	0.452187i	$0.850644\pi$
$252$	−2.79656	−0.176167
$253$	−3.40667	−0.214175
$254$	−19.3815	−1.21611
$255$	15.0352	0.941540
$256$	1.00000	0.0625000
$257$	−11.5197	−0.718576	−0.359288	−	0.933227i	$-0.616980\pi$
$257$	−11.5197	−0.718576	−0.359288	+	0.933227i	$0.616980\pi$
$258$	8.36030	0.520490
$259$	3.35526	0.208486
$260$	0.636880	0.0394976
$261$	14.2711	0.883357
$262$	−4.99933	−0.308860
$263$	26.6852	1.64548	0.822740	−	0.568418i	$-0.192445\pi$
$263$	26.6852	1.64548	0.822740	+	0.568418i	$0.192445\pi$
$264$	2.85095	0.175464
$265$	21.1668	1.30027
$266$	0	0
$267$	−4.52428	−0.276881
$268$	8.30406	0.507251
$269$	−2.07333	−0.126413	−0.0632065	−	0.998000i	$-0.520133\pi$
$269$	−2.07333	−0.126413	−0.0632065	+	0.998000i	$0.520133\pi$
$270$	−0.862765	−0.0525062
$271$	−23.0985	−1.40314	−0.701568	−	0.712602i	$-0.747516\pi$
$271$	−23.0985	−1.40314	−0.701568	+	0.712602i	$0.747516\pi$
$272$	3.54532	0.214967
$273$	−0.870512	−0.0526858
$274$	20.8876	1.26187
$275$	−2.24671	−0.135482
$276$	−6.92645	−0.416923
$277$	20.3780	1.22440	0.612198	−	0.790705i	$-0.290286\pi$
$277$	20.3780	1.22440	0.612198	+	0.790705i	$0.290286\pi$
$278$	−13.2393	−0.794042
$279$	−3.86351	−0.231302
$280$	−1.76144	−0.105266
$281$	15.6633	0.934394	0.467197	−	0.884153i	$-0.345264\pi$
$281$	15.6633	0.934394	0.467197	+	0.884153i	$0.345264\pi$
$282$	27.9690	1.66553
$283$	2.37228	0.141017	0.0705086	−	0.997511i	$-0.477538\pi$
$283$	2.37228	0.141017	0.0705086	+	0.997511i	$0.477538\pi$
$284$	−0.226733	−0.0134541
$285$	0	0
$286$	0.428148	0.0253169
$287$	−10.0120	−0.590987
$288$	2.79656	0.164789
$289$	−4.43067	−0.260628
$290$	8.98876	0.527838
$291$	−9.62478	−0.564215
$292$	−14.0163	−0.820242
$293$	−0.586563	−0.0342674	−0.0171337	−	0.999853i	$-0.505454\pi$
$293$	−0.586563	−0.0342674	−0.0171337	+	0.999853i	$0.505454\pi$
$294$	2.40760	0.140414
$295$	−13.6113	−0.792478
$296$	−3.35526	−0.195021
$297$	−0.580001	−0.0336551
$298$	3.08216	0.178545
$299$	−1.04020	−0.0601561
$300$	−4.56803	−0.263735
$301$	−3.47246	−0.200149
$302$	−6.35364	−0.365611
$303$	−44.9358	−2.58150
$304$	0	0
$305$	−3.50601	−0.200754
$306$	9.91471	0.566786
$307$	19.9202	1.13690	0.568452	−	0.822717i	$-0.307543\pi$
$307$	19.9202	1.13690	0.568452	+	0.822717i	$0.307543\pi$
$308$	−1.18414	−0.0674728
$309$	−5.66376	−0.322200
$310$	−2.43347	−0.138212
$311$	−14.6345	−0.829849	−0.414925	−	0.909856i	$-0.636192\pi$
$311$	−14.6345	−0.829849	−0.414925	+	0.909856i	$0.636192\pi$
$312$	0.870512	0.0492831
$313$	−26.9261	−1.52195	−0.760975	−	0.648781i	$-0.775279\pi$
$313$	−26.9261	−1.52195	−0.760975	+	0.648781i	$0.775279\pi$
$314$	4.20918	0.237538
$315$	−4.92597	−0.277547
$316$	5.28063	0.297059
$317$	30.5772	1.71739	0.858694	−	0.512489i	$-0.171276\pi$
$317$	30.5772	1.71739	0.858694	+	0.512489i	$0.171276\pi$
$318$	28.9316	1.62241
$319$	6.04278	0.338331
$320$	1.76144	0.0984674
$321$	−7.50816	−0.419065
$322$	2.87691	0.160324
$323$	0	0
$324$	−9.56894	−0.531608
$325$	−0.686015	−0.0380533
$326$	7.15678	0.396377
$327$	−34.1483	−1.88840
$328$	10.0120	0.552818
$329$	−11.6169	−0.640463
$330$	5.02177	0.276439
$331$	20.3542	1.11877	0.559384	−	0.828909i	$-0.311038\pi$
$331$	20.3542	1.11877	0.559384	+	0.828909i	$0.311038\pi$
$332$	13.3912	0.734939
$333$	−9.38319	−0.514196
$334$	22.1964	1.21454
$335$	14.6271	0.799164
$336$	−2.40760	−0.131346
$337$	−14.8090	−0.806700	−0.403350	−	0.915046i	$-0.632154\pi$
$337$	−14.8090	−0.806700	−0.403350	+	0.915046i	$0.632154\pi$
$338$	−12.8693	−0.699996
$339$	−9.19910	−0.499627
$340$	6.24487	0.338676
$341$	−1.63592	−0.0885900
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	3.47246	0.187222
$345$	−12.2005	−0.656854
$346$	10.8227	0.581832
$347$	−19.0467	−1.02248	−0.511241	−	0.859438i	$-0.670814\pi$
$347$	−19.0467	−1.02248	−0.511241	+	0.859438i	$0.670814\pi$
$348$	12.2862	0.658609
$349$	−21.1239	−1.13074	−0.565368	−	0.824839i	$-0.691266\pi$
$349$	−21.1239	−1.13074	−0.565368	+	0.824839i	$0.691266\pi$
$350$	1.89733	0.101417
$351$	−0.177098	−0.00945282
$352$	1.18414	0.0631150
$353$	2.24313	0.119390	0.0596949	−	0.998217i	$-0.480987\pi$
$353$	2.24313	0.119390	0.0596949	+	0.998217i	$0.480987\pi$
$354$	−18.6044	−0.988813
$355$	−0.399377	−0.0211967
$356$	−1.87916	−0.0995954
$357$	−8.53574	−0.451759
$358$	−11.7586	−0.621462
$359$	3.31981	0.175213	0.0876066	−	0.996155i	$-0.472078\pi$
$359$	3.31981	0.175213	0.0876066	+	0.996155i	$0.472078\pi$
$360$	4.92597	0.259621
$361$	0	0
$362$	1.62634	0.0854787
$363$	−23.1077	−1.21284
$364$	−0.361568	−0.0189513
$365$	−24.6888	−1.29227
$366$	−4.79215	−0.250490
$367$	−18.3886	−0.959875	−0.479938	−	0.877303i	$-0.659341\pi$
$367$	−18.3886	−0.959875	−0.479938	+	0.877303i	$0.659341\pi$
$368$	−2.87691	−0.149969
$369$	27.9990	1.45757
$370$	−5.91009	−0.307251
$371$	−12.0168	−0.623880
$372$	−3.32616	−0.172453
$373$	−3.33060	−0.172452	−0.0862259	−	0.996276i	$-0.527481\pi$
$373$	−3.33060	−0.172452	−0.0862259	+	0.996276i	$0.527481\pi$
$374$	4.19817	0.217082
$375$	−29.2505	−1.51049
$376$	11.6169	0.599098
$377$	1.84511	0.0950280
$378$	0.489807	0.0251929
$379$	30.8785	1.58612	0.793061	−	0.609142i	$-0.208486\pi$
$379$	30.8785	1.58612	0.793061	+	0.609142i	$0.208486\pi$
$380$	0	0
$381$	−46.6631	−2.39062
$382$	15.1136	0.773281
$383$	−4.18785	−0.213989	−0.106995	−	0.994260i	$-0.534123\pi$
$383$	−4.18785	−0.213989	−0.106995	+	0.994260i	$0.534123\pi$
$384$	2.40760	0.122863
$385$	−2.08580	−0.106302
$386$	−21.0053	−1.06914
$387$	9.71093	0.493634
$388$	−3.99766	−0.202950
$389$	13.7229	0.695779	0.347890	−	0.937536i	$-0.386898\pi$
$389$	13.7229	0.695779	0.347890	+	0.937536i	$0.386898\pi$
$390$	1.53335	0.0776444
$391$	−10.1996	−0.515814
$392$	1.00000	0.0505076
$393$	−12.0364	−0.607157
$394$	−24.5580	−1.23722
$395$	9.30151	0.468010
$396$	3.31153	0.166410
$397$	−12.7243	−0.638614	−0.319307	−	0.947651i	$-0.603450\pi$
$397$	−12.7243	−0.638614	−0.319307	+	0.947651i	$0.603450\pi$
$398$	5.50367	0.275874
$399$	0	0
$400$	−1.89733	−0.0948667
$401$	27.5174	1.37415	0.687077	−	0.726585i	$-0.258894\pi$
$401$	27.5174	1.37415	0.687077	+	0.726585i	$0.258894\pi$
$402$	19.9929	0.997155
$403$	−0.499514	−0.0248826
$404$	−18.6641	−0.928575
$405$	−16.8551	−0.837536
$406$	−5.10308	−0.253262
$407$	−3.97311	−0.196940
$408$	8.53574	0.422582
$409$	30.1566	1.49115	0.745574	−	0.666423i	$-0.232175\pi$
$409$	30.1566	1.49115	0.745574	+	0.666423i	$0.232175\pi$
$410$	17.6355	0.870953
$411$	50.2892	2.48058
$412$	−2.35245	−0.115897
$413$	7.72735	0.380238
$414$	−8.04544	−0.395412
$415$	23.5878	1.15788
$416$	0.361568	0.0177273
$417$	−31.8750	−1.56093
$418$	0	0
$419$	25.2631	1.23418	0.617092	−	0.786891i	$-0.288311\pi$
$419$	25.2631	1.23418	0.617092	+	0.786891i	$0.288311\pi$
$420$	−4.24085	−0.206932
$421$	−38.0387	−1.85389	−0.926945	−	0.375197i	$-0.877575\pi$
$421$	−38.0387	−1.85389	−0.926945	+	0.375197i	$0.877575\pi$
$422$	4.53017	0.220525
$423$	32.4875	1.57959
$424$	12.0168	0.583586
$425$	−6.72666	−0.326291
$426$	−0.545884	−0.0264482
$427$	1.99042	0.0963234
$428$	−3.11852	−0.150739
$429$	1.03081	0.0497680
$430$	6.11652	0.294965
$431$	18.9095	0.910837	0.455419	−	0.890277i	$-0.349490\pi$
$431$	18.9095	0.910837	0.455419	+	0.890277i	$0.349490\pi$
$432$	−0.489807	−0.0235658
$433$	−12.6102	−0.606009	−0.303005	−	0.952989i	$-0.597990\pi$
$433$	−12.6102	−0.606009	−0.303005	+	0.952989i	$0.597990\pi$
$434$	1.38152	0.0663152
$435$	21.6414	1.03763
$436$	−14.1835	−0.679266
$437$	0	0
$438$	−33.7457	−1.61243
$439$	33.9256	1.61918	0.809591	−	0.586994i	$-0.199689\pi$
$439$	33.9256	1.61918	0.809591	+	0.586994i	$0.199689\pi$
$440$	2.08580	0.0994364
$441$	2.79656	0.133169
$442$	1.28188	0.0609726
$443$	−4.69792	−0.223205	−0.111602	−	0.993753i	$-0.535598\pi$
$443$	−4.69792	−0.223205	−0.111602	+	0.993753i	$0.535598\pi$
$444$	−8.07815	−0.383372
$445$	−3.31003	−0.156910
$446$	10.0211	0.474515
$447$	7.42061	0.350983
$448$	−1.00000	−0.0472456
$449$	25.3251	1.19517	0.597583	−	0.801807i	$-0.296128\pi$
$449$	25.3251	1.19517	0.597583	+	0.801807i	$0.296128\pi$
$450$	−5.30600	−0.250127
$451$	11.8556	0.558258
$452$	−3.82085	−0.179718
$453$	−15.2970	−0.718718
$454$	−7.43478	−0.348931
$455$	−0.636880	−0.0298574
$456$	0	0
$457$	−40.3466	−1.88734	−0.943668	−	0.330894i	$-0.892650\pi$
$457$	−40.3466	−1.88734	−0.943668	+	0.330894i	$0.892650\pi$
$458$	3.96142	0.185105
$459$	−1.73652	−0.0810540
$460$	−5.06749	−0.236273
$461$	8.28479	0.385861	0.192931	−	0.981212i	$-0.438201\pi$
$461$	8.28479	0.385861	0.192931	+	0.981212i	$0.438201\pi$
$462$	−2.85095	−0.132638
$463$	−26.7426	−1.24283	−0.621416	−	0.783481i	$-0.713442\pi$
$463$	−26.7426	−1.24283	−0.621416	+	0.783481i	$0.713442\pi$
$464$	5.10308	0.236905
$465$	−5.85882	−0.271696
$466$	−14.3859	−0.666414
$467$	7.29907	0.337761	0.168880	−	0.985637i	$-0.445985\pi$
$467$	7.29907	0.337761	0.168880	+	0.985637i	$0.445985\pi$
$468$	1.01115	0.0467402
$469$	−8.30406	−0.383446
$470$	20.4625	0.943866
$471$	10.1340	0.466952
$472$	−7.72735	−0.355680
$473$	4.11189	0.189065
$474$	12.7137	0.583959
$475$	0	0
$476$	−3.54532	−0.162500
$477$	33.6056	1.53870
$478$	−7.12027	−0.325673
$479$	−27.1804	−1.24191	−0.620953	−	0.783848i	$-0.713254\pi$
$479$	−27.1804	−1.24191	−0.620953	+	0.783848i	$0.713254\pi$
$480$	4.24085	0.193567
$481$	−1.21316	−0.0553151
$482$	−14.9816	−0.682394
$483$	6.92645	0.315165
$484$	−9.59781	−0.436264
$485$	−7.04163	−0.319744
$486$	−21.5688	−0.978380
$487$	6.88190	0.311849	0.155924	−	0.987769i	$-0.450164\pi$
$487$	6.88190	0.311849	0.155924	+	0.987769i	$0.450164\pi$
$488$	−1.99042	−0.0901023
$489$	17.2307	0.779199
$490$	1.76144	0.0795737
$491$	−9.47678	−0.427681	−0.213841	−	0.976869i	$-0.568597\pi$
$491$	−9.47678	−0.427681	−0.213841	+	0.976869i	$0.568597\pi$
$492$	24.1048	1.08673
$493$	18.0921	0.814826
$494$	0	0
$495$	5.83305	0.262176
$496$	−1.38152	−0.0620322
$497$	0.226733	0.0101704
$498$	32.2408	1.44474
$499$	−5.58793	−0.250150	−0.125075	−	0.992147i	$-0.539917\pi$
$499$	−5.58793	−0.250150	−0.125075	+	0.992147i	$0.539917\pi$
$500$	−12.1492	−0.543330
$501$	53.4403	2.38753
$502$	−28.2614	−1.26137
$503$	−9.98556	−0.445234	−0.222617	−	0.974906i	$-0.571460\pi$
$503$	−9.98556	−0.445234	−0.222617	+	0.974906i	$0.571460\pi$
$504$	−2.79656	−0.124569
$505$	−32.8757	−1.46295
$506$	−3.40667	−0.151445
$507$	−30.9841	−1.37605
$508$	−19.3815	−0.859917
$509$	−35.5061	−1.57378	−0.786890	−	0.617093i	$-0.788310\pi$
$509$	−35.5061	−1.57378	−0.786890	+	0.617093i	$0.788310\pi$
$510$	15.0352	0.665769
$511$	14.0163	0.620044
$512$	1.00000	0.0441942
$513$	0	0
$514$	−11.5197	−0.508110
$515$	−4.14369	−0.182593
$516$	8.36030	0.368042
$517$	13.7561	0.604993
$518$	3.35526	0.147422
$519$	26.0568	1.14377
$520$	0.636880	0.0279290
$521$	4.29772	0.188287	0.0941433	−	0.995559i	$-0.469989\pi$
$521$	4.29772	0.188287	0.0941433	+	0.995559i	$0.469989\pi$
$522$	14.2711	0.624627
$523$	31.1762	1.36324	0.681620	−	0.731707i	$-0.261276\pi$
$523$	31.1762	1.36324	0.681620	+	0.731707i	$0.261276\pi$
$524$	−4.99933	−0.218397
$525$	4.56803	0.199365
$526$	26.6852	1.16353
$527$	−4.89794	−0.213358
$528$	2.85095	0.124072
$529$	−14.7234	−0.640148
$530$	21.1668	0.919428
$531$	−21.6100	−0.937794
$532$	0	0
$533$	3.62000	0.156800
$534$	−4.52428	−0.195785
$535$	−5.49308	−0.237487
$536$	8.30406	0.358681
$537$	−28.3101	−1.22167
$538$	−2.07333	−0.0893874
$539$	1.18414	0.0510047
$540$	−0.862765	−0.0371275
$541$	−5.51854	−0.237261	−0.118630	−	0.992938i	$-0.537850\pi$
$541$	−5.51854	−0.237261	−0.118630	+	0.992938i	$0.537850\pi$
$542$	−23.0985	−0.992167
$543$	3.91559	0.168034
$544$	3.54532	0.152005
$545$	−24.9834	−1.07017
$546$	−0.870512	−0.0372545
$547$	8.52743	0.364607	0.182303	−	0.983242i	$-0.441645\pi$
$547$	8.52743	0.364607	0.182303	+	0.983242i	$0.441645\pi$
$548$	20.8876	0.892276
$549$	−5.56634	−0.237565
$550$	−2.24671	−0.0958002
$551$	0	0
$552$	−6.92645	−0.294809
$553$	−5.28063	−0.224555
$554$	20.3780	0.865778
$555$	−14.2292	−0.603994
$556$	−13.2393	−0.561472
$557$	22.8183	0.966843	0.483422	−	0.875388i	$-0.339394\pi$
$557$	22.8183	0.966843	0.483422	+	0.875388i	$0.339394\pi$
$558$	−3.86351	−0.163555
$559$	1.25553	0.0531032
$560$	−1.76144	−0.0744344
$561$	10.1075	0.426740
$562$	15.6633	0.660716
$563$	10.7974	0.455056	0.227528	−	0.973772i	$-0.426936\pi$
$563$	10.7974	0.455056	0.227528	+	0.973772i	$0.426936\pi$
$564$	27.9690	1.17771
$565$	−6.73020	−0.283142
$566$	2.37228	0.0997142
$567$	9.56894	0.401858
$568$	−0.226733	−0.00951351
$569$	5.10510	0.214017	0.107008	−	0.994258i	$-0.465873\pi$
$569$	5.10510	0.214017	0.107008	+	0.994258i	$0.465873\pi$
$570$	0	0
$571$	4.62174	0.193414	0.0967070	−	0.995313i	$-0.469169\pi$
$571$	4.62174	0.193414	0.0967070	+	0.995313i	$0.469169\pi$
$572$	0.428148	0.0179018
$573$	36.3877	1.52012
$574$	−10.0120	−0.417891
$575$	5.45845	0.227633
$576$	2.79656	0.116523
$577$	−32.4426	−1.35060	−0.675302	−	0.737541i	$-0.735987\pi$
$577$	−32.4426	−1.35060	−0.675302	+	0.737541i	$0.735987\pi$
$578$	−4.43067	−0.184292
$579$	−50.5725	−2.10172
$580$	8.98876	0.373238
$581$	−13.3912	−0.555562
$582$	−9.62478	−0.398960
$583$	14.2296	0.589329
$584$	−14.0163	−0.579998
$585$	1.78107	0.0736382
$586$	−0.586563	−0.0242307
$587$	−7.36820	−0.304118	−0.152059	−	0.988371i	$-0.548590\pi$
$587$	−7.36820	−0.304118	−0.152059	+	0.988371i	$0.548590\pi$
$588$	2.40760	0.0992879
$589$	0	0
$590$	−13.6113	−0.560367
$591$	−59.1261	−2.43212
$592$	−3.35526	−0.137900
$593$	3.98443	0.163621	0.0818105	−	0.996648i	$-0.473930\pi$
$593$	3.98443	0.163621	0.0818105	+	0.996648i	$0.473930\pi$
$594$	−0.580001	−0.0237977
$595$	−6.24487	−0.256015
$596$	3.08216	0.126250
$597$	13.2507	0.542314
$598$	−1.04020	−0.0425368
$599$	4.19582	0.171436	0.0857182	−	0.996319i	$-0.472682\pi$
$599$	4.19582	0.171436	0.0857182	+	0.996319i	$0.472682\pi$
$600$	−4.56803	−0.186489
$601$	30.5991	1.24816	0.624081	−	0.781360i	$-0.285474\pi$
$601$	30.5991	1.24816	0.624081	+	0.781360i	$0.285474\pi$
$602$	−3.47246	−0.141527
$603$	23.2228	0.945706
$604$	−6.35364	−0.258526
$605$	−16.9059	−0.687324
$606$	−44.9358	−1.82539
$607$	42.8583	1.73957	0.869783	−	0.493435i	$-0.164259\pi$
$607$	42.8583	1.73957	0.869783	+	0.493435i	$0.164259\pi$
$608$	0	0
$609$	−12.2862	−0.497862
$610$	−3.50601	−0.141954
$611$	4.20031	0.169926
$612$	9.91471	0.400778
$613$	24.8978	1.00561	0.502806	−	0.864399i	$-0.332301\pi$
$613$	24.8978	1.00561	0.502806	+	0.864399i	$0.332301\pi$
$614$	19.9202	0.803912
$615$	42.4592	1.71212
$616$	−1.18414	−0.0477105
$617$	13.1675	0.530102	0.265051	−	0.964234i	$-0.414611\pi$
$617$	13.1675	0.530102	0.265051	+	0.964234i	$0.414611\pi$
$618$	−5.66376	−0.227830
$619$	−5.34109	−0.214676	−0.107338	−	0.994223i	$-0.534233\pi$
$619$	−5.34109	−0.214676	−0.107338	+	0.994223i	$0.534233\pi$
$620$	−2.43347	−0.0977303
$621$	1.40913	0.0565464
$622$	−14.6345	−0.586792
$623$	1.87916	0.0752870
$624$	0.870512	0.0348484
$625$	−11.9135	−0.476538
$626$	−26.9261	−1.07618
$627$	0	0
$628$	4.20918	0.167965
$629$	−11.8955	−0.474305
$630$	−4.92597	−0.196255
$631$	−49.2604	−1.96103	−0.980513	−	0.196453i	$-0.937058\pi$
$631$	−49.2604	−1.96103	−0.980513	+	0.196453i	$0.937058\pi$
$632$	5.28063	0.210052
$633$	10.9069	0.433509
$634$	30.5772	1.21438
$635$	−34.1394	−1.35478
$636$	28.9316	1.14721
$637$	0.361568	0.0143258
$638$	6.04278	0.239236
$639$	−0.634073	−0.0250835
$640$	1.76144	0.0696270
$641$	−34.2166	−1.35147	−0.675737	−	0.737143i	$-0.736174\pi$
$641$	−34.2166	−1.35147	−0.675737	+	0.737143i	$0.736174\pi$
$642$	−7.50816	−0.296324
$643$	−44.9211	−1.77152	−0.885758	−	0.464148i	$-0.846361\pi$
$643$	−44.9211	−1.77152	−0.885758	+	0.464148i	$0.846361\pi$
$644$	2.87691	0.113366
$645$	14.7262	0.579842
$646$	0	0
$647$	19.1593	0.753230	0.376615	−	0.926370i	$-0.377088\pi$
$647$	19.1593	0.753230	0.376615	+	0.926370i	$0.377088\pi$
$648$	−9.56894	−0.375903
$649$	−9.15029	−0.359180
$650$	−0.686015	−0.0269077
$651$	3.32616	0.130362
$652$	7.15678	0.280281
$653$	26.2846	1.02860	0.514299	−	0.857611i	$-0.328052\pi$
$653$	26.2846	1.02860	0.514299	+	0.857611i	$0.328052\pi$
$654$	−34.1483	−1.33530
$655$	−8.80602	−0.344079
$656$	10.0120	0.390901
$657$	−39.1974	−1.52924
$658$	−11.6169	−0.452876
$659$	−37.2268	−1.45015	−0.725074	−	0.688671i	$-0.758195\pi$
$659$	−37.2268	−1.45015	−0.725074	+	0.688671i	$0.758195\pi$
$660$	5.02177	0.195472
$661$	10.9786	0.427018	0.213509	−	0.976941i	$-0.431511\pi$
$661$	10.9786	0.427018	0.213509	+	0.976941i	$0.431511\pi$
$662$	20.3542	0.791089
$663$	3.08625	0.119860
$664$	13.3912	0.519681
$665$	0	0
$666$	−9.38319	−0.363591
$667$	−14.6811	−0.568454
$668$	22.1964	0.858806
$669$	24.1270	0.932802
$670$	14.6271	0.565094
$671$	−2.35695	−0.0909889
$672$	−2.40760	−0.0928754
$673$	7.09081	0.273331	0.136665	−	0.990617i	$-0.456362\pi$
$673$	7.09081	0.273331	0.136665	+	0.990617i	$0.456362\pi$
$674$	−14.8090	−0.570423
$675$	0.929327	0.0357698
$676$	−12.8693	−0.494972
$677$	−4.66569	−0.179317	−0.0896584	−	0.995973i	$-0.528578\pi$
$677$	−4.66569	−0.179317	−0.0896584	+	0.995973i	$0.528578\pi$
$678$	−9.19910	−0.353289
$679$	3.99766	0.153416
$680$	6.24487	0.239480
$681$	−17.9000	−0.685930
$682$	−1.63592	−0.0626426
$683$	−33.2650	−1.27285	−0.636425	−	0.771338i	$-0.719588\pi$
$683$	−33.2650	−1.27285	−0.636425	+	0.771338i	$0.719588\pi$
$684$	0	0
$685$	36.7923	1.40576
$686$	−1.00000	−0.0381802
$687$	9.53753	0.363880
$688$	3.47246	0.132386
$689$	4.34488	0.165527
$690$	−12.2005	−0.464466
$691$	27.5209	1.04694	0.523472	−	0.852043i	$-0.324637\pi$
$691$	27.5209	1.04694	0.523472	+	0.852043i	$0.324637\pi$
$692$	10.8227	0.411418
$693$	−3.31153	−0.125794
$694$	−19.0467	−0.723004
$695$	−23.3203	−0.884588
$696$	12.2862	0.465707
$697$	35.4956	1.34449
$698$	−21.1239	−0.799550
$699$	−34.6356	−1.31004
$700$	1.89733	0.0717125
$701$	6.21171	0.234613	0.117306	−	0.993096i	$-0.462574\pi$
$701$	6.21171	0.234613	0.117306	+	0.993096i	$0.462574\pi$
$702$	−0.177098	−0.00668415
$703$	0	0
$704$	1.18414	0.0446291
$705$	49.2657	1.85545
$706$	2.24313	0.0844213
$707$	18.6641	0.701937
$708$	−18.6044	−0.699196
$709$	−1.17736	−0.0442167	−0.0221083	−	0.999756i	$-0.507038\pi$
$709$	−1.17736	−0.0442167	−0.0221083	+	0.999756i	$0.507038\pi$
$710$	−0.399377	−0.0149883
$711$	14.7676	0.553828
$712$	−1.87916	−0.0704246
$713$	3.97451	0.148847
$714$	−8.53574	−0.319442
$715$	0.754157	0.0282039
$716$	−11.7586	−0.439440
$717$	−17.1428	−0.640209
$718$	3.31981	0.123894
$719$	37.2872	1.39058	0.695289	−	0.718730i	$-0.255276\pi$
$719$	37.2872	1.39058	0.695289	+	0.718730i	$0.255276\pi$
$720$	4.92597	0.183580
$721$	2.35245	0.0876097
$722$	0	0
$723$	−36.0698	−1.34145
$724$	1.62634	0.0604426
$725$	−9.68225	−0.359590
$726$	−23.1077	−0.857608
$727$	17.8760	0.662983	0.331492	−	0.943458i	$-0.392448\pi$
$727$	17.8760	0.662983	0.331492	+	0.943458i	$0.392448\pi$
$728$	−0.361568	−0.0134006
$729$	−23.2223	−0.860085
$730$	−24.6888	−0.913775
$731$	12.3110	0.455338
$732$	−4.79215	−0.177123
$733$	7.02123	0.259335	0.129667	−	0.991558i	$-0.458609\pi$
$733$	7.02123	0.259335	0.129667	+	0.991558i	$0.458609\pi$
$734$	−18.3886	−0.678734
$735$	4.24085	0.156426
$736$	−2.87691	−0.106044
$737$	9.83320	0.362211
$738$	27.9990	1.03066
$739$	−46.3549	−1.70519	−0.852596	−	0.522570i	$-0.824973\pi$
$739$	−46.3549	−1.70519	−0.852596	+	0.522570i	$0.824973\pi$
$740$	−5.91009	−0.217259
$741$	0	0
$742$	−12.0168	−0.441150
$743$	11.0899	0.406850	0.203425	−	0.979091i	$-0.434793\pi$
$743$	11.0899	0.406850	0.203425	+	0.979091i	$0.434793\pi$
$744$	−3.32616	−0.121943
$745$	5.42903	0.198904
$746$	−3.33060	−0.121942
$747$	37.4494	1.37020
$748$	4.19817	0.153500
$749$	3.11852	0.113948
$750$	−29.2505	−1.06808
$751$	16.6367	0.607080	0.303540	−	0.952819i	$-0.401831\pi$
$751$	16.6367	0.607080	0.303540	+	0.952819i	$0.401831\pi$
$752$	11.6169	0.423626
$753$	−68.0424	−2.47960
$754$	1.84511	0.0671949
$755$	−11.1915	−0.407302
$756$	0.489807	0.0178141
$757$	−23.9144	−0.869185	−0.434592	−	0.900627i	$-0.643108\pi$
$757$	−23.9144	−0.869185	−0.434592	+	0.900627i	$0.643108\pi$
$758$	30.8785	1.12156
$759$	−8.20191	−0.297711
$760$	0	0
$761$	50.6040	1.83439	0.917196	−	0.398435i	$-0.130447\pi$
$761$	50.6040	1.83439	0.917196	+	0.398435i	$0.130447\pi$
$762$	−46.6631	−1.69042
$763$	14.1835	0.513477
$764$	15.1136	0.546792
$765$	17.4641	0.631418
$766$	−4.18785	−0.151313
$767$	−2.79396	−0.100884
$768$	2.40760	0.0868769
$769$	−8.66228	−0.312370	−0.156185	−	0.987728i	$-0.549920\pi$
$769$	−8.66228	−0.312370	−0.156185	+	0.987728i	$0.549920\pi$
$770$	−2.08580	−0.0751669
$771$	−27.7348	−0.998843
$772$	−21.0053	−0.755998
$773$	28.4345	1.02272	0.511358	−	0.859368i	$-0.329142\pi$
$773$	28.4345	1.02272	0.511358	+	0.859368i	$0.329142\pi$
$774$	9.71093	0.349052
$775$	2.62121	0.0941566
$776$	−3.99766	−0.143508
$777$	8.07815	0.289802
$778$	13.7229	0.491990
$779$	0	0
$780$	1.53335	0.0549029
$781$	−0.268485	−0.00960713
$782$	−10.1996	−0.364736
$783$	−2.49952	−0.0893257
$784$	1.00000	0.0357143
$785$	7.41422	0.264625
$786$	−12.0364	−0.429325
$787$	7.80328	0.278157	0.139078	−	0.990281i	$-0.455586\pi$
$787$	7.80328	0.278157	0.139078	+	0.990281i	$0.455586\pi$
$788$	−24.5580	−0.874844
$789$	64.2474	2.28727
$790$	9.30151	0.330933
$791$	3.82085	0.135854
$792$	3.31153	0.117670
$793$	−0.719673	−0.0255564
$794$	−12.7243	−0.451568
$795$	50.9613	1.80741
$796$	5.50367	0.195073
$797$	22.7219	0.804849	0.402425	−	0.915453i	$-0.368168\pi$
$797$	22.7219	0.804849	0.402425	+	0.915453i	$0.368168\pi$
$798$	0	0
$799$	41.1858	1.45705
$800$	−1.89733	−0.0670809
$801$	−5.25519	−0.185683
$802$	27.5174	0.971673
$803$	−16.5973	−0.585706
$804$	19.9929	0.705095
$805$	5.06749	0.178606
$806$	−0.499514	−0.0175946
$807$	−4.99175	−0.175718
$808$	−18.6641	−0.656602
$809$	−4.48771	−0.157779	−0.0788897	−	0.996883i	$-0.525137\pi$
$809$	−4.48771	−0.157779	−0.0788897	+	0.996883i	$0.525137\pi$
$810$	−16.8551	−0.592228
$811$	−17.5040	−0.614648	−0.307324	−	0.951605i	$-0.599434\pi$
$811$	−17.5040	−0.614648	−0.307324	+	0.951605i	$0.599434\pi$
$812$	−5.10308	−0.179083
$813$	−55.6121	−1.95040
$814$	−3.97311	−0.139258
$815$	12.6062	0.441577
$816$	8.53574	0.298811
$817$	0	0
$818$	30.1566	1.05440
$819$	−1.01115	−0.0353323
$820$	17.6355	0.615857
$821$	9.51661	0.332132	0.166066	−	0.986115i	$-0.446893\pi$
$821$	9.51661	0.332132	0.166066	+	0.986115i	$0.446893\pi$
$822$	50.2892	1.75404
$823$	31.8532	1.11033	0.555167	−	0.831739i	$-0.312654\pi$
$823$	31.8532	1.11033	0.555167	+	0.831739i	$0.312654\pi$
$824$	−2.35245	−0.0819513
$825$	−5.40920	−0.188324
$826$	7.72735	0.268869
$827$	10.9457	0.380620	0.190310	−	0.981724i	$-0.439051\pi$
$827$	10.9457	0.380620	0.190310	+	0.981724i	$0.439051\pi$
$828$	−8.04544	−0.279598
$829$	−30.2531	−1.05073	−0.525366	−	0.850876i	$-0.676072\pi$
$829$	−30.2531	−1.05073	−0.525366	+	0.850876i	$0.676072\pi$
$830$	23.5878	0.818746
$831$	49.0622	1.70195
$832$	0.361568	0.0125351
$833$	3.54532	0.122838
$834$	−31.8750	−1.10374
$835$	39.0977	1.35303
$836$	0	0
$837$	0.676679	0.0233894
$838$	25.2631	0.872699
$839$	38.9311	1.34405	0.672025	−	0.740528i	$-0.265425\pi$
$839$	38.9311	1.34405	0.672025	+	0.740528i	$0.265425\pi$
$840$	−4.24085	−0.146323
$841$	−2.95857	−0.102020
$842$	−38.0387	−1.31090
$843$	37.7110	1.29884
$844$	4.53017	0.155935
$845$	−22.6684	−0.779818
$846$	32.4875	1.11694
$847$	9.59781	0.329784
$848$	12.0168	0.412658
$849$	5.71150	0.196018
$850$	−6.72666	−0.230723
$851$	9.65278	0.330893
$852$	−0.545884	−0.0187017
$853$	−40.9671	−1.40269	−0.701344	−	0.712823i	$-0.747416\pi$
$853$	−40.9671	−1.40269	−0.701344	+	0.712823i	$0.747416\pi$
$854$	1.99042	0.0681109
$855$	0	0
$856$	−3.11852	−0.106589
$857$	−13.0672	−0.446367	−0.223184	−	0.974776i	$-0.571645\pi$
$857$	−13.0672	−0.446367	−0.223184	+	0.974776i	$0.571645\pi$
$858$	1.03081	0.0351913
$859$	14.8518	0.506735	0.253368	−	0.967370i	$-0.418462\pi$
$859$	14.8518	0.506735	0.253368	+	0.967370i	$0.418462\pi$
$860$	6.11652	0.208572
$861$	−24.1048	−0.821491
$862$	18.9095	0.644059
$863$	−56.6176	−1.92729	−0.963643	−	0.267193i	$-0.913904\pi$
$863$	−56.6176	−1.92729	−0.963643	+	0.267193i	$0.913904\pi$
$864$	−0.489807	−0.0166636
$865$	19.0635	0.648180
$866$	−12.6102	−0.428513
$867$	−10.6673	−0.362281
$868$	1.38152	0.0468919
$869$	6.25303	0.212119
$870$	21.6414	0.733712
$871$	3.00248	0.101735
$872$	−14.1835	−0.480314
$873$	−11.1797	−0.378375
$874$	0	0
$875$	12.1492	0.410719
$876$	−33.7457	−1.14016
$877$	−29.6812	−1.00226	−0.501131	−	0.865372i	$-0.667082\pi$
$877$	−29.6812	−1.00226	−0.501131	+	0.865372i	$0.667082\pi$
$878$	33.9256	1.14494
$879$	−1.41221	−0.0476327
$880$	2.08580	0.0703122
$881$	−21.9013	−0.737875	−0.368937	−	0.929454i	$-0.620278\pi$
$881$	−21.9013	−0.737875	−0.368937	+	0.929454i	$0.620278\pi$
$882$	2.79656	0.0941650
$883$	−22.8216	−0.768008	−0.384004	−	0.923331i	$-0.625455\pi$
$883$	−22.8216	−0.768008	−0.384004	+	0.923331i	$0.625455\pi$
$884$	1.28188	0.0431141
$885$	−32.7705	−1.10157
$886$	−4.69792	−0.157830
$887$	19.8209	0.665519	0.332760	−	0.943012i	$-0.392020\pi$
$887$	19.8209	0.665519	0.332760	+	0.943012i	$0.392020\pi$
$888$	−8.07815	−0.271085
$889$	19.3815	0.650036
$890$	−3.31003	−0.110952
$891$	−11.3310	−0.379602
$892$	10.0211	0.335533
$893$	0	0
$894$	7.42061	0.248182
$895$	−20.7121	−0.692329
$896$	−1.00000	−0.0334077
$897$	−2.50438	−0.0836189
$898$	25.3251	0.845109
$899$	−7.05002	−0.235131
$900$	−5.30600	−0.176867
$901$	42.6034	1.41932
$902$	11.8556	0.394748
$903$	−8.36030	−0.278213
$904$	−3.82085	−0.127080
$905$	2.86470	0.0952260
$906$	−15.2970	−0.508210
$907$	−51.2543	−1.70187	−0.850936	−	0.525270i	$-0.823965\pi$
$907$	−51.2543	−1.70187	−0.850936	+	0.525270i	$0.823965\pi$
$908$	−7.43478	−0.246732
$909$	−52.1953	−1.73121
$910$	−0.636880	−0.0211124
$911$	−31.5849	−1.04646	−0.523228	−	0.852193i	$-0.675272\pi$
$911$	−31.5849	−1.04646	−0.523228	+	0.852193i	$0.675272\pi$
$912$	0	0
$913$	15.8571	0.524795
$914$	−40.3466	−1.33455
$915$	−8.44108	−0.279054
$916$	3.96142	0.130889
$917$	4.99933	0.165092
$918$	−1.73652	−0.0573138
$919$	−9.70848	−0.320253	−0.160127	−	0.987096i	$-0.551190\pi$
$919$	−9.70848	−0.320253	−0.160127	+	0.987096i	$0.551190\pi$
$920$	−5.06749	−0.167070
$921$	47.9599	1.58033
$922$	8.28479	0.272845
$923$	−0.0819794	−0.00269839
$924$	−2.85095	−0.0937893
$925$	6.36605	0.209315
$926$	−26.7426	−0.878815
$927$	−6.57875	−0.216075
$928$	5.10308	0.167517
$929$	−11.8253	−0.387977	−0.193988	−	0.981004i	$-0.562142\pi$
$929$	−11.8253	−0.387977	−0.193988	+	0.981004i	$0.562142\pi$
$930$	−5.85882	−0.192118
$931$	0	0
$932$	−14.3859	−0.471226
$933$	−35.2342	−1.15352
$934$	7.29907	0.238833
$935$	7.39482	0.241837
$936$	1.01115	0.0330503
$937$	39.1239	1.27812	0.639062	−	0.769155i	$-0.279323\pi$
$937$	39.1239	1.27812	0.639062	+	0.769155i	$0.279323\pi$
$938$	−8.30406	−0.271137
$939$	−64.8273	−2.11556
$940$	20.4625	0.667414
$941$	16.5733	0.540274	0.270137	−	0.962822i	$-0.412931\pi$
$941$	16.5733	0.540274	0.270137	+	0.962822i	$0.412931\pi$
$942$	10.1340	0.330185
$943$	−28.8035	−0.937970
$944$	−7.72735	−0.251504
$945$	0.862765	0.0280657
$946$	4.11189	0.133689
$947$	27.0746	0.879805	0.439902	−	0.898046i	$-0.355013\pi$
$947$	27.0746	0.879805	0.439902	+	0.898046i	$0.355013\pi$
$948$	12.7137	0.412921
$949$	−5.06784	−0.164509
$950$	0	0
$951$	73.6178	2.38722
$952$	−3.54532	−0.114905
$953$	−23.7483	−0.769284	−0.384642	−	0.923066i	$-0.625675\pi$
$953$	−23.7483	−0.769284	−0.384642	+	0.923066i	$0.625675\pi$
$954$	33.6056	1.08802
$955$	26.6218	0.861460
$956$	−7.12027	−0.230286
$957$	14.5486	0.470290
$958$	−27.1804	−0.878160
$959$	−20.8876	−0.674497
$960$	4.24085	0.136873
$961$	−29.0914	−0.938432
$962$	−1.21316	−0.0391137
$963$	−8.72113	−0.281034
$964$	−14.9816	−0.482525
$965$	−36.9996	−1.19106
$966$	6.92645	0.222855
$967$	43.7978	1.40844	0.704221	−	0.709981i	$-0.251297\pi$
$967$	43.7978	1.40844	0.704221	+	0.709981i	$0.251297\pi$
$968$	−9.59781	−0.308485
$969$	0	0
$970$	−7.04163	−0.226093
$971$	17.3224	0.555901	0.277951	−	0.960595i	$-0.410345\pi$
$971$	17.3224	0.555901	0.277951	+	0.960595i	$0.410345\pi$
$972$	−21.5688	−0.691819
$973$	13.2393	0.424433
$974$	6.88190	0.220510
$975$	−1.65165	−0.0528952
$976$	−1.99042	−0.0637119
$977$	−55.2674	−1.76816	−0.884080	−	0.467336i	$-0.845214\pi$
$977$	−55.2674	−1.76816	−0.884080	+	0.467336i	$0.845214\pi$
$978$	17.2307	0.550977
$979$	−2.22520	−0.0711176
$980$	1.76144	0.0562671
$981$	−39.6650	−1.26641
$982$	−9.47678	−0.302416
$983$	−15.1410	−0.482922	−0.241461	−	0.970411i	$-0.577627\pi$
$983$	−15.1410	−0.482922	−0.241461	+	0.970411i	$0.577627\pi$
$984$	24.1048	0.768434
$985$	−43.2575	−1.37830
$986$	18.0921	0.576169
$987$	−27.9690	−0.890263
$988$	0	0
$989$	−9.98994	−0.317662
$990$	5.83305	0.185386
$991$	−32.4171	−1.02976	−0.514882	−	0.857261i	$-0.672164\pi$
$991$	−32.4171	−1.02976	−0.514882	+	0.857261i	$0.672164\pi$
$992$	−1.38152	−0.0438634
$993$	49.0049	1.55512
$994$	0.226733	0.00719154
$995$	9.69439	0.307333
$996$	32.2408	1.02159
$997$	49.4268	1.56536	0.782681	−	0.622423i	$-0.213852\pi$
$997$	49.4268	1.56536	0.782681	+	0.622423i	$0.213852\pi$
$998$	−5.58793	−0.176883
$999$	1.64343	0.0519959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bi.1.7	yes	8
19.18	odd	2		5054.2.a.bf.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.bf.1.2	✓	8	19.18	odd	2
5054.2.a.bi.1.7	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.40760 q^{3} +1.00000 q^{4} +1.76144 q^{5} +2.40760 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.79656 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.40760 q^{3} +1.00000 q^{4} +1.76144 q^{5} +2.40760 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.79656 q^{9} +1.76144 q^{10} +1.18414 q^{11} +2.40760 q^{12} +0.361568 q^{13} -1.00000 q^{14} +4.24085 q^{15} +1.00000 q^{16} +3.54532 q^{17} +2.79656 q^{18} +1.76144 q^{20} -2.40760 q^{21} +1.18414 q^{22} -2.87691 q^{23} +2.40760 q^{24} -1.89733 q^{25} +0.361568 q^{26} -0.489807 q^{27} -1.00000 q^{28} +5.10308 q^{29} +4.24085 q^{30} -1.38152 q^{31} +1.00000 q^{32} +2.85095 q^{33} +3.54532 q^{34} -1.76144 q^{35} +2.79656 q^{36} -3.35526 q^{37} +0.870512 q^{39} +1.76144 q^{40} +10.0120 q^{41} -2.40760 q^{42} +3.47246 q^{43} +1.18414 q^{44} +4.92597 q^{45} -2.87691 q^{46} +11.6169 q^{47} +2.40760 q^{48} +1.00000 q^{49} -1.89733 q^{50} +8.53574 q^{51} +0.361568 q^{52} +12.0168 q^{53} -0.489807 q^{54} +2.08580 q^{55} -1.00000 q^{56} +5.10308 q^{58} -7.72735 q^{59} +4.24085 q^{60} -1.99042 q^{61} -1.38152 q^{62} -2.79656 q^{63} +1.00000 q^{64} +0.636880 q^{65} +2.85095 q^{66} +8.30406 q^{67} +3.54532 q^{68} -6.92645 q^{69} -1.76144 q^{70} -0.226733 q^{71} +2.79656 q^{72} -14.0163 q^{73} -3.35526 q^{74} -4.56803 q^{75} -1.18414 q^{77} +0.870512 q^{78} +5.28063 q^{79} +1.76144 q^{80} -9.56894 q^{81} +10.0120 q^{82} +13.3912 q^{83} -2.40760 q^{84} +6.24487 q^{85} +3.47246 q^{86} +12.2862 q^{87} +1.18414 q^{88} -1.87916 q^{89} +4.92597 q^{90} -0.361568 q^{91} -2.87691 q^{92} -3.32616 q^{93} +11.6169 q^{94} +2.40760 q^{96} -3.99766 q^{97} +1.00000 q^{98} +3.31153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{10} + 4 q^{11} + 4 q^{12} + 6 q^{13} - 8 q^{14} + 8 q^{15} + 8 q^{16} + 2 q^{17} + 8 q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{22} + 20 q^{23} + 4 q^{24} - 8 q^{25} + 6 q^{26} + 22 q^{27} - 8 q^{28} + 16 q^{29} + 8 q^{30} + 22 q^{31} + 8 q^{32} - 8 q^{33} + 2 q^{34} - 6 q^{35} + 8 q^{36} - 12 q^{37} + 8 q^{39} + 6 q^{40} + 36 q^{41} - 4 q^{42} + 4 q^{44} - 4 q^{45} + 20 q^{46} + 6 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} - 4 q^{51} + 6 q^{52} + 16 q^{53} + 22 q^{54} + 18 q^{55} - 8 q^{56} + 16 q^{58} + 14 q^{59} + 8 q^{60} + 10 q^{61} + 22 q^{62} - 8 q^{63} + 8 q^{64} + 32 q^{65} - 8 q^{66} - 20 q^{67} + 2 q^{68} + 40 q^{69} - 6 q^{70} + 8 q^{72} - 18 q^{73} - 12 q^{74} + 16 q^{75} - 4 q^{77} + 8 q^{78} + 4 q^{79} + 6 q^{80} + 12 q^{81} + 36 q^{82} + 36 q^{83} - 4 q^{84} - 16 q^{85} + 28 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{90} - 6 q^{91} + 20 q^{92} + 16 q^{93} + 6 q^{94} + 4 q^{96} + 26 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^10 + 4 * q^11 + 4 * q^12 + 6 * q^13 - 8 * q^14 + 8 * q^15 + 8 * q^16 + 2 * q^17 + 8 * q^18 + 6 * q^20 - 4 * q^21 + 4 * q^22 + 20 * q^23 + 4 * q^24 - 8 * q^25 + 6 * q^26 + 22 * q^27 - 8 * q^28 + 16 * q^29 + 8 * q^30 + 22 * q^31 + 8 * q^32 - 8 * q^33 + 2 * q^34 - 6 * q^35 + 8 * q^36 - 12 * q^37 + 8 * q^39 + 6 * q^40 + 36 * q^41 - 4 * q^42 + 4 * q^44 - 4 * q^45 + 20 * q^46 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 - 4 * q^51 + 6 * q^52 + 16 * q^53 + 22 * q^54 + 18 * q^55 - 8 * q^56 + 16 * q^58 + 14 * q^59 + 8 * q^60 + 10 * q^61 + 22 * q^62 - 8 * q^63 + 8 * q^64 + 32 * q^65 - 8 * q^66 - 20 * q^67 + 2 * q^68 + 40 * q^69 - 6 * q^70 + 8 * q^72 - 18 * q^73 - 12 * q^74 + 16 * q^75 - 4 * q^77 + 8 * q^78 + 4 * q^79 + 6 * q^80 + 12 * q^81 + 36 * q^82 + 36 * q^83 - 4 * q^84 - 16 * q^85 + 28 * q^87 + 4 * q^88 + 18 * q^89 - 4 * q^90 - 6 * q^91 + 20 * q^92 + 16 * q^93 + 6 * q^94 + 4 * q^96 + 26 * q^97 + 8 * q^98 + 4 * q^99

Introduction

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