LMFDB - Embedded newform 6014.2.a.i.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.289255 q^{3} +1.00000 q^{4} -1.50320 q^{5} -0.289255 q^{6} -2.57965 q^{7} +1.00000 q^{8} -2.91633 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.289255 q^{3} +1.00000 q^{4} -1.50320 q^{5} -0.289255 q^{6} -2.57965 q^{7} +1.00000 q^{8} -2.91633 q^{9} -1.50320 q^{10} -5.43643 q^{11} -0.289255 q^{12} -1.47624 q^{13} -2.57965 q^{14} +0.434806 q^{15} +1.00000 q^{16} +1.57612 q^{17} -2.91633 q^{18} -4.90373 q^{19} -1.50320 q^{20} +0.746176 q^{21} -5.43643 q^{22} +6.21910 q^{23} -0.289255 q^{24} -2.74040 q^{25} -1.47624 q^{26} +1.71133 q^{27} -2.57965 q^{28} +5.70422 q^{29} +0.434806 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.57251 q^{33} +1.57612 q^{34} +3.87772 q^{35} -2.91633 q^{36} -5.74001 q^{37} -4.90373 q^{38} +0.427010 q^{39} -1.50320 q^{40} +7.81619 q^{41} +0.746176 q^{42} -5.87231 q^{43} -5.43643 q^{44} +4.38382 q^{45} +6.21910 q^{46} -5.18606 q^{47} -0.289255 q^{48} -0.345405 q^{49} -2.74040 q^{50} -0.455900 q^{51} -1.47624 q^{52} -8.60020 q^{53} +1.71133 q^{54} +8.17202 q^{55} -2.57965 q^{56} +1.41843 q^{57} +5.70422 q^{58} +10.6138 q^{59} +0.434806 q^{60} +12.5325 q^{61} -1.00000 q^{62} +7.52312 q^{63} +1.00000 q^{64} +2.21908 q^{65} +1.57251 q^{66} -6.89530 q^{67} +1.57612 q^{68} -1.79890 q^{69} +3.87772 q^{70} +16.6916 q^{71} -2.91633 q^{72} -9.02889 q^{73} -5.74001 q^{74} +0.792674 q^{75} -4.90373 q^{76} +14.0241 q^{77} +0.427010 q^{78} -1.95061 q^{79} -1.50320 q^{80} +8.25399 q^{81} +7.81619 q^{82} +15.3506 q^{83} +0.746176 q^{84} -2.36921 q^{85} -5.87231 q^{86} -1.64997 q^{87} -5.43643 q^{88} -15.2682 q^{89} +4.38382 q^{90} +3.80819 q^{91} +6.21910 q^{92} +0.289255 q^{93} -5.18606 q^{94} +7.37126 q^{95} -0.289255 q^{96} -1.00000 q^{97} -0.345405 q^{98} +15.8544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.289255	−0.167001	−0.0835006	−	0.996508i	$-0.526610\pi$
$3$	−0.289255	−0.167001	−0.0835006	+	0.996508i	$0.526610\pi$
$4$	1.00000	0.500000
$5$	−1.50320	−0.672249	−0.336125	−	0.941817i	$-0.609116\pi$
$5$	−1.50320	−0.672249	−0.336125	+	0.941817i	$0.609116\pi$
$6$	−0.289255	−0.118088
$7$	−2.57965	−0.975016	−0.487508	−	0.873118i	$-0.662094\pi$
$7$	−2.57965	−0.975016	−0.487508	+	0.873118i	$0.662094\pi$
$8$	1.00000	0.353553
$9$	−2.91633	−0.972111
$10$	−1.50320	−0.475352
$11$	−5.43643	−1.63915	−0.819573	−	0.572975i	$-0.805789\pi$
$11$	−5.43643	−1.63915	−0.819573	+	0.572975i	$0.805789\pi$
$12$	−0.289255	−0.0835006
$13$	−1.47624	−0.409436	−0.204718	−	0.978821i	$-0.565628\pi$
$13$	−1.47624	−0.409436	−0.204718	+	0.978821i	$0.565628\pi$
$14$	−2.57965	−0.689440
$15$	0.434806	0.112266
$16$	1.00000	0.250000
$17$	1.57612	0.382265	0.191133	−	0.981564i	$-0.438784\pi$
$17$	1.57612	0.382265	0.191133	+	0.981564i	$0.438784\pi$
$18$	−2.91633	−0.687386
$19$	−4.90373	−1.12499	−0.562496	−	0.826800i	$-0.690159\pi$
$19$	−4.90373	−1.12499	−0.562496	+	0.826800i	$0.690159\pi$
$20$	−1.50320	−0.336125
$21$	0.746176	0.162829
$22$	−5.43643	−1.15905
$23$	6.21910	1.29677	0.648386	−	0.761312i	$-0.275444\pi$
$23$	6.21910	1.29677	0.648386	+	0.761312i	$0.275444\pi$
$24$	−0.289255	−0.0590439
$25$	−2.74040	−0.548081
$26$	−1.47624	−0.289515
$27$	1.71133	0.329345
$28$	−2.57965	−0.487508
$29$	5.70422	1.05925	0.529623	−	0.848233i	$-0.322333\pi$
$29$	5.70422	1.05925	0.529623	+	0.848233i	$0.322333\pi$
$30$	0.434806	0.0793844
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	1.57251	0.273739
$34$	1.57612	0.270302
$35$	3.87772	0.655454
$36$	−2.91633	−0.486055
$37$	−5.74001	−0.943652	−0.471826	−	0.881692i	$-0.656405\pi$
$37$	−5.74001	−0.943652	−0.471826	+	0.881692i	$0.656405\pi$
$38$	−4.90373	−0.795489
$39$	0.427010	0.0683763
$40$	−1.50320	−0.237676
$41$	7.81619	1.22068	0.610342	−	0.792138i	$-0.291032\pi$
$41$	7.81619	1.22068	0.610342	+	0.792138i	$0.291032\pi$
$42$	0.746176	0.115137
$43$	−5.87231	−0.895519	−0.447760	−	0.894154i	$-0.647778\pi$
$43$	−5.87231	−0.895519	−0.447760	+	0.894154i	$0.647778\pi$
$44$	−5.43643	−0.819573
$45$	4.38382	0.653501
$46$	6.21910	0.916956
$47$	−5.18606	−0.756465	−0.378233	−	0.925711i	$-0.623468\pi$
$47$	−5.18606	−0.756465	−0.378233	+	0.925711i	$0.623468\pi$
$48$	−0.289255	−0.0417503
$49$	−0.345405	−0.0493436
$50$	−2.74040	−0.387552
$51$	−0.455900	−0.0638387
$52$	−1.47624	−0.204718
$53$	−8.60020	−1.18133	−0.590664	−	0.806918i	$-0.701134\pi$
$53$	−8.60020	−1.18133	−0.590664	+	0.806918i	$0.701134\pi$
$54$	1.71133	0.232882
$55$	8.17202	1.10192
$56$	−2.57965	−0.344720
$57$	1.41843	0.187875
$58$	5.70422	0.749001
$59$	10.6138	1.38179	0.690897	−	0.722954i	$-0.257216\pi$
$59$	10.6138	1.38179	0.690897	+	0.722954i	$0.257216\pi$
$60$	0.434806	0.0561332
$61$	12.5325	1.60462	0.802312	−	0.596905i	$-0.203603\pi$
$61$	12.5325	1.60462	0.802312	+	0.596905i	$0.203603\pi$
$62$	−1.00000	−0.127000
$63$	7.52312	0.947823
$64$	1.00000	0.125000
$65$	2.21908	0.275243
$66$	1.57251	0.193563
$67$	−6.89530	−0.842395	−0.421197	−	0.906969i	$-0.638390\pi$
$67$	−6.89530	−0.842395	−0.421197	+	0.906969i	$0.638390\pi$
$68$	1.57612	0.191133
$69$	−1.79890	−0.216562
$70$	3.87772	0.463476
$71$	16.6916	1.98093	0.990464	−	0.137773i	$-0.0439944\pi$
$71$	16.6916	1.98093	0.990464	+	0.137773i	$0.0439944\pi$
$72$	−2.91633	−0.343693
$73$	−9.02889	−1.05675	−0.528376	−	0.849010i	$-0.677199\pi$
$73$	−9.02889	−1.05675	−0.528376	+	0.849010i	$0.677199\pi$
$74$	−5.74001	−0.667263
$75$	0.792674	0.0915302
$76$	−4.90373	−0.562496
$77$	14.0241	1.59819
$78$	0.427010	0.0483494
$79$	−1.95061	−0.219460	−0.109730	−	0.993961i	$-0.534999\pi$
$79$	−1.95061	−0.219460	−0.109730	+	0.993961i	$0.534999\pi$
$80$	−1.50320	−0.168062
$81$	8.25399	0.917110
$82$	7.81619	0.863154
$83$	15.3506	1.68495	0.842474	−	0.538738i	$-0.181099\pi$
$83$	15.3506	1.68495	0.842474	+	0.538738i	$0.181099\pi$
$84$	0.746176	0.0814144
$85$	−2.36921	−0.256977
$86$	−5.87231	−0.633228
$87$	−1.64997	−0.176896
$88$	−5.43643	−0.579526
$89$	−15.2682	−1.61843	−0.809213	−	0.587515i	$-0.800106\pi$
$89$	−15.2682	−1.61843	−0.809213	+	0.587515i	$0.800106\pi$
$90$	4.38382	0.462095
$91$	3.80819	0.399207
$92$	6.21910	0.648386
$93$	0.289255	0.0299943
$94$	−5.18606	−0.534902
$95$	7.37126	0.756275
$96$	−0.289255	−0.0295219
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−0.345405	−0.0348912
$99$	15.8544	1.59343
$100$	−2.74040	−0.274040
$101$	−15.2230	−1.51475	−0.757373	−	0.652982i	$-0.773518\pi$
$101$	−15.2230	−1.51475	−0.757373	+	0.652982i	$0.773518\pi$
$102$	−0.455900	−0.0451408
$103$	−6.16248	−0.607207	−0.303604	−	0.952798i	$-0.598190\pi$
$103$	−6.16248	−0.607207	−0.303604	+	0.952798i	$0.598190\pi$
$104$	−1.47624	−0.144757
$105$	−1.12165	−0.109462
$106$	−8.60020	−0.835325
$107$	0.356049	0.0344205	0.0172103	−	0.999852i	$-0.494522\pi$
$107$	0.356049	0.0344205	0.0172103	+	0.999852i	$0.494522\pi$
$108$	1.71133	0.164672
$109$	10.4557	1.00147	0.500736	−	0.865600i	$-0.333063\pi$
$109$	10.4557	1.00147	0.500736	+	0.865600i	$0.333063\pi$
$110$	8.17202	0.779172
$111$	1.66032	0.157591
$112$	−2.57965	−0.243754
$113$	3.47736	0.327122	0.163561	−	0.986533i	$-0.447702\pi$
$113$	3.47736	0.327122	0.163561	+	0.986533i	$0.447702\pi$
$114$	1.41843	0.132848
$115$	−9.34852	−0.871754
$116$	5.70422	0.529623
$117$	4.30521	0.398017
$118$	10.6138	0.977075
$119$	−4.06584	−0.372715
$120$	0.434806	0.0396922
$121$	18.5548	1.68680
$122$	12.5325	1.13464
$123$	−2.26087	−0.203856
$124$	−1.00000	−0.0898027
$125$	11.6353	1.04070
$126$	7.52312	0.670212
$127$	17.9293	1.59097	0.795483	−	0.605976i	$-0.207217\pi$
$127$	17.9293	1.59097	0.795483	+	0.605976i	$0.207217\pi$
$128$	1.00000	0.0883883
$129$	1.69859	0.149553
$130$	2.21908	0.194626
$131$	14.9218	1.30373	0.651863	−	0.758337i	$-0.273988\pi$
$131$	14.9218	1.30373	0.651863	+	0.758337i	$0.273988\pi$
$132$	1.57251	0.136870
$133$	12.6499	1.09689
$134$	−6.89530	−0.595663
$135$	−2.57246	−0.221402
$136$	1.57612	0.135151
$137$	21.6850	1.85268	0.926338	−	0.376695i	$-0.122939\pi$
$137$	21.6850	1.85268	0.926338	+	0.376695i	$0.122939\pi$
$138$	−1.79890	−0.153133
$139$	16.5913	1.40726	0.703629	−	0.710567i	$-0.251562\pi$
$139$	16.5913	1.40726	0.703629	+	0.710567i	$0.251562\pi$
$140$	3.87772	0.327727
$141$	1.50009	0.126331
$142$	16.6916	1.40073
$143$	8.02549	0.671125
$144$	−2.91633	−0.243028
$145$	−8.57455	−0.712078
$146$	−9.02889	−0.747237
$147$	0.0999101	0.00824044
$148$	−5.74001	−0.471826
$149$	3.32560	0.272444	0.136222	−	0.990678i	$-0.456504\pi$
$149$	3.32560	0.272444	0.136222	+	0.990678i	$0.456504\pi$
$150$	0.792674	0.0647216
$151$	−15.8717	−1.29162	−0.645809	−	0.763499i	$-0.723480\pi$
$151$	−15.8717	−1.29162	−0.645809	+	0.763499i	$0.723480\pi$
$152$	−4.90373	−0.397745
$153$	−4.59649	−0.371604
$154$	14.0241	1.13009
$155$	1.50320	0.120740
$156$	0.427010	0.0341882
$157$	−8.53394	−0.681083	−0.340541	−	0.940230i	$-0.610610\pi$
$157$	−8.53394	−0.681083	−0.340541	+	0.940230i	$0.610610\pi$
$158$	−1.95061	−0.155182
$159$	2.48765	0.197283
$160$	−1.50320	−0.118838
$161$	−16.0431	−1.26437
$162$	8.25399	0.648494
$163$	12.7620	0.999595	0.499798	−	0.866142i	$-0.333408\pi$
$163$	12.7620	0.999595	0.499798	+	0.866142i	$0.333408\pi$
$164$	7.81619	0.610342
$165$	−2.36379	−0.184021
$166$	15.3506	1.19144
$167$	4.99869	0.386810	0.193405	−	0.981119i	$-0.438047\pi$
$167$	4.99869	0.386810	0.193405	+	0.981119i	$0.438047\pi$
$168$	0.746176	0.0575687
$169$	−10.8207	−0.832362
$170$	−2.36921	−0.181710
$171$	14.3009	1.09362
$172$	−5.87231	−0.447760
$173$	−23.1216	−1.75790	−0.878952	−	0.476911i	$-0.841757\pi$
$173$	−23.1216	−1.75790	−0.878952	+	0.476911i	$0.841757\pi$
$174$	−1.64997	−0.125084
$175$	7.06928	0.534388
$176$	−5.43643	−0.409787
$177$	−3.07008	−0.230761
$178$	−15.2682	−1.14440
$179$	19.4036	1.45029	0.725145	−	0.688596i	$-0.241773\pi$
$179$	19.4036	1.45029	0.725145	+	0.688596i	$0.241773\pi$
$180$	4.38382	0.326750
$181$	−7.36447	−0.547397	−0.273698	−	0.961816i	$-0.588247\pi$
$181$	−7.36447	−0.547397	−0.273698	+	0.961816i	$0.588247\pi$
$182$	3.80819	0.282282
$183$	−3.62509	−0.267974
$184$	6.21910	0.458478
$185$	8.62836	0.634369
$186$	0.289255	0.0212092
$187$	−8.56847	−0.626588
$188$	−5.18606	−0.378233
$189$	−4.41462	−0.321117
$190$	7.37126	0.534767
$191$	−18.3355	−1.32671	−0.663353	−	0.748306i	$-0.730867\pi$
$191$	−18.3355	−1.32671	−0.663353	+	0.748306i	$0.730867\pi$
$192$	−0.289255	−0.0208752
$193$	2.84754	0.204970	0.102485	−	0.994735i	$-0.467321\pi$
$193$	2.84754	0.204970	0.102485	+	0.994735i	$0.467321\pi$
$194$	−1.00000	−0.0717958
$195$	−0.641879	−0.0459659
$196$	−0.345405	−0.0246718
$197$	11.8675	0.845526	0.422763	−	0.906240i	$-0.361060\pi$
$197$	11.8675	0.845526	0.422763	+	0.906240i	$0.361060\pi$
$198$	15.8544	1.12673
$199$	−13.1064	−0.929086	−0.464543	−	0.885551i	$-0.653781\pi$
$199$	−13.1064	−0.929086	−0.464543	+	0.885551i	$0.653781\pi$
$200$	−2.74040	−0.193776
$201$	1.99450	0.140681
$202$	−15.2230	−1.07109
$203$	−14.7149	−1.03278
$204$	−0.455900	−0.0319194
$205$	−11.7493	−0.820604
$206$	−6.16248	−0.429360
$207$	−18.1369	−1.26060
$208$	−1.47624	−0.102359
$209$	26.6588	1.84403
$210$	−1.12165	−0.0774011
$211$	14.2400	0.980325	0.490162	−	0.871631i	$-0.336937\pi$
$211$	14.2400	0.980325	0.490162	+	0.871631i	$0.336937\pi$
$212$	−8.60020	−0.590664
$213$	−4.82812	−0.330817
$214$	0.356049	0.0243390
$215$	8.82723	0.602012
$216$	1.71133	0.116441
$217$	2.57965	0.175118
$218$	10.4557	0.708147
$219$	2.61165	0.176479
$220$	8.17202	0.550958
$221$	−2.32673	−0.156513
$222$	1.66032	0.111434
$223$	−17.0203	−1.13976	−0.569882	−	0.821727i	$-0.693011\pi$
$223$	−17.0203	−1.13976	−0.569882	+	0.821727i	$0.693011\pi$
$224$	−2.57965	−0.172360
$225$	7.99193	0.532795
$226$	3.47736	0.231311
$227$	12.7620	0.847045	0.423522	−	0.905886i	$-0.360793\pi$
$227$	12.7620	0.847045	0.423522	+	0.905886i	$0.360793\pi$
$228$	1.41843	0.0939375
$229$	14.1584	0.935614	0.467807	−	0.883831i	$-0.345044\pi$
$229$	14.1584	0.935614	0.467807	+	0.883831i	$0.345044\pi$
$230$	−9.34852	−0.616423
$231$	−4.05653	−0.266900
$232$	5.70422	0.374500
$233$	15.1467	0.992292	0.496146	−	0.868239i	$-0.334748\pi$
$233$	15.1467	0.992292	0.496146	+	0.868239i	$0.334748\pi$
$234$	4.30521	0.281441
$235$	7.79567	0.508533
$236$	10.6138	0.690897
$237$	0.564222	0.0366502
$238$	−4.06584	−0.263549
$239$	−19.3227	−1.24988	−0.624942	−	0.780672i	$-0.714877\pi$
$239$	−19.3227	−1.24988	−0.624942	+	0.780672i	$0.714877\pi$
$240$	0.434806	0.0280666
$241$	−7.59597	−0.489299	−0.244650	−	0.969612i	$-0.578673\pi$
$241$	−7.59597	−0.489299	−0.244650	+	0.969612i	$0.578673\pi$
$242$	18.5548	1.19275
$243$	−7.52148	−0.482503
$244$	12.5325	0.802312
$245$	0.519212	0.0331712
$246$	−2.26087	−0.144148
$247$	7.23909	0.460612
$248$	−1.00000	−0.0635001
$249$	−4.44023	−0.281388
$250$	11.6353	0.735883
$251$	−15.2888	−0.965023	−0.482511	−	0.875890i	$-0.660275\pi$
$251$	−15.2888	−0.965023	−0.482511	+	0.875890i	$0.660275\pi$
$252$	7.52312	0.473912
$253$	−33.8097	−2.12560
$254$	17.9293	1.12498
$255$	0.685306	0.0429155
$256$	1.00000	0.0625000
$257$	3.84806	0.240035	0.120018	−	0.992772i	$-0.461705\pi$
$257$	3.84806	0.240035	0.120018	+	0.992772i	$0.461705\pi$
$258$	1.69859	0.105750
$259$	14.8072	0.920076
$260$	2.21908	0.137622
$261$	−16.6354	−1.02970
$262$	14.9218	0.921873
$263$	−23.9276	−1.47544	−0.737719	−	0.675108i	$-0.764097\pi$
$263$	−23.9276	−1.47544	−0.737719	+	0.675108i	$0.764097\pi$
$264$	1.57251	0.0967815
$265$	12.9278	0.794147
$266$	12.6499	0.775615
$267$	4.41640	0.270279
$268$	−6.89530	−0.421197
$269$	−26.9454	−1.64289	−0.821445	−	0.570287i	$-0.806832\pi$
$269$	−26.9454	−1.64289	−0.821445	+	0.570287i	$0.806832\pi$
$270$	−2.57246	−0.156555
$271$	23.3843	1.42050	0.710248	−	0.703952i	$-0.248583\pi$
$271$	23.3843	1.42050	0.710248	+	0.703952i	$0.248583\pi$
$272$	1.57612	0.0955663
$273$	−1.10154	−0.0666680
$274$	21.6850	1.31004
$275$	14.8980	0.898385
$276$	−1.79890	−0.108281
$277$	−14.2148	−0.854082	−0.427041	−	0.904232i	$-0.640444\pi$
$277$	−14.2148	−0.854082	−0.427041	+	0.904232i	$0.640444\pi$
$278$	16.5913	0.995082
$279$	2.91633	0.174596
$280$	3.87772	0.231738
$281$	−10.5957	−0.632087	−0.316043	−	0.948745i	$-0.602355\pi$
$281$	−10.5957	−0.632087	−0.316043	+	0.948745i	$0.602355\pi$
$282$	1.50009	0.0893292
$283$	−2.34298	−0.139276	−0.0696379	−	0.997572i	$-0.522184\pi$
$283$	−2.34298	−0.139276	−0.0696379	+	0.997572i	$0.522184\pi$
$284$	16.6916	0.990464
$285$	−2.13217	−0.126299
$286$	8.02549	0.474557
$287$	−20.1630	−1.19019
$288$	−2.91633	−0.171846
$289$	−14.5158	−0.853873
$290$	−8.57455	−0.503515
$291$	0.289255	0.0169564
$292$	−9.02889	−0.528376
$293$	9.50205	0.555115	0.277558	−	0.960709i	$-0.410475\pi$
$293$	9.50205	0.555115	0.277558	+	0.960709i	$0.410475\pi$
$294$	0.0999101	0.00582687
$295$	−15.9545	−0.928910
$296$	−5.74001	−0.333631
$297$	−9.30351	−0.539844
$298$	3.32560	0.192647
$299$	−9.18089	−0.530945
$300$	0.792674	0.0457651
$301$	15.1485	0.873146
$302$	−15.8717	−0.913312
$303$	4.40333	0.252965
$304$	−4.90373	−0.281248
$305$	−18.8388	−1.07871
$306$	−4.59649	−0.262764
$307$	10.0935	0.576064	0.288032	−	0.957621i	$-0.406999\pi$
$307$	10.0935	0.576064	0.288032	+	0.957621i	$0.406999\pi$
$308$	14.0241	0.799097
$309$	1.78253	0.101404
$310$	1.50320	0.0853758
$311$	26.7523	1.51699	0.758493	−	0.651681i	$-0.225936\pi$
$311$	26.7523	1.51699	0.758493	+	0.651681i	$0.225936\pi$
$312$	0.427010	0.0241747
$313$	16.1257	0.911476	0.455738	−	0.890114i	$-0.349375\pi$
$313$	16.1257	0.911476	0.455738	+	0.890114i	$0.349375\pi$
$314$	−8.53394	−0.481598
$315$	−11.3087	−0.637174
$316$	−1.95061	−0.109730
$317$	0.604638	0.0339598	0.0169799	−	0.999856i	$-0.494595\pi$
$317$	0.604638	0.0339598	0.0169799	+	0.999856i	$0.494595\pi$
$318$	2.48765	0.139500
$319$	−31.0106	−1.73626
$320$	−1.50320	−0.0840312
$321$	−0.102989	−0.00574827
$322$	−16.0431	−0.894047
$323$	−7.72885	−0.430045
$324$	8.25399	0.458555
$325$	4.04550	0.224404
$326$	12.7620	0.706821
$327$	−3.02435	−0.167247
$328$	7.81619	0.431577
$329$	13.3782	0.737566
$330$	−2.36379	−0.130123
$331$	15.3115	0.841598	0.420799	−	0.907154i	$-0.361750\pi$
$331$	15.3115	0.841598	0.420799	+	0.907154i	$0.361750\pi$
$332$	15.3506	0.842474
$333$	16.7398	0.917334
$334$	4.99869	0.273516
$335$	10.3650	0.566300
$336$	0.746176	0.0407072
$337$	10.0245	0.546068	0.273034	−	0.962004i	$-0.411973\pi$
$337$	10.0245	0.546068	0.273034	+	0.962004i	$0.411973\pi$
$338$	−10.8207	−0.588569
$339$	−1.00584	−0.0546299
$340$	−2.36921	−0.128489
$341$	5.43643	0.294399
$342$	14.3009	0.773304
$343$	18.9486	1.02313
$344$	−5.87231	−0.316614
$345$	2.70410	0.145584
$346$	−23.1216	−1.24303
$347$	−2.36918	−0.127184	−0.0635921	−	0.997976i	$-0.520256\pi$
$347$	−2.36918	−0.127184	−0.0635921	+	0.997976i	$0.520256\pi$
$348$	−1.64997	−0.0884478
$349$	19.2788	1.03197	0.515986	−	0.856597i	$-0.327426\pi$
$349$	19.2788	1.03197	0.515986	+	0.856597i	$0.327426\pi$
$350$	7.06928	0.377869
$351$	−2.52633	−0.134846
$352$	−5.43643	−0.289763
$353$	−22.5343	−1.19938	−0.599691	−	0.800232i	$-0.704710\pi$
$353$	−22.5343	−1.19938	−0.599691	+	0.800232i	$0.704710\pi$
$354$	−3.07008	−0.163173
$355$	−25.0907	−1.33168
$356$	−15.2682	−0.809213
$357$	1.17606	0.0622438
$358$	19.4036	1.02551
$359$	−0.258059	−0.0136198	−0.00680990	−	0.999977i	$-0.502168\pi$
$359$	−0.258059	−0.0136198	−0.00680990	+	0.999977i	$0.502168\pi$
$360$	4.38382	0.231047
$361$	5.04652	0.265606
$362$	−7.36447	−0.387068
$363$	−5.36706	−0.281698
$364$	3.80819	0.199603
$365$	13.5722	0.710401
$366$	−3.62509	−0.189486
$367$	−35.9593	−1.87706	−0.938529	−	0.345199i	$-0.887811\pi$
$367$	−35.9593	−1.87706	−0.938529	+	0.345199i	$0.887811\pi$
$368$	6.21910	0.324193
$369$	−22.7946	−1.18664
$370$	8.62836	0.448567
$371$	22.1855	1.15181
$372$	0.289255	0.0149972
$373$	28.4290	1.47200	0.735999	−	0.676983i	$-0.236713\pi$
$373$	28.4290	1.47200	0.735999	+	0.676983i	$0.236713\pi$
$374$	−8.56847	−0.443065
$375$	−3.36558	−0.173798
$376$	−5.18606	−0.267451
$377$	−8.42081	−0.433694
$378$	−4.41462	−0.227064
$379$	5.01658	0.257684	0.128842	−	0.991665i	$-0.458874\pi$
$379$	5.01658	0.257684	0.128842	+	0.991665i	$0.458874\pi$
$380$	7.37126	0.378138
$381$	−5.18613	−0.265693
$382$	−18.3355	−0.938123
$383$	−0.233452	−0.0119289	−0.00596443	−	0.999982i	$-0.501899\pi$
$383$	−0.233452	−0.0119289	−0.00596443	+	0.999982i	$0.501899\pi$
$384$	−0.289255	−0.0147610
$385$	−21.0810	−1.07438
$386$	2.84754	0.144936
$387$	17.1256	0.870544
$388$	−1.00000	−0.0507673
$389$	−10.9885	−0.557139	−0.278570	−	0.960416i	$-0.589860\pi$
$389$	−10.9885	−0.557139	−0.278570	+	0.960416i	$0.589860\pi$
$390$	−0.641879	−0.0325028
$391$	9.80204	0.495710
$392$	−0.345405	−0.0174456
$393$	−4.31620	−0.217724
$394$	11.8675	0.597877
$395$	2.93214	0.147532
$396$	15.8544	0.796716
$397$	21.7365	1.09092	0.545461	−	0.838136i	$-0.316355\pi$
$397$	21.7365	1.09092	0.545461	+	0.838136i	$0.316355\pi$
$398$	−13.1064	−0.656963
$399$	−3.65904	−0.183181
$400$	−2.74040	−0.137020
$401$	−30.5399	−1.52509	−0.762546	−	0.646934i	$-0.776051\pi$
$401$	−30.5399	−1.52509	−0.762546	+	0.646934i	$0.776051\pi$
$402$	1.99450	0.0994765
$403$	1.47624	0.0735369
$404$	−15.2230	−0.757373
$405$	−12.4074	−0.616526
$406$	−14.7149	−0.730288
$407$	31.2052	1.54678
$408$	−0.455900	−0.0225704
$409$	−6.39927	−0.316424	−0.158212	−	0.987405i	$-0.550573\pi$
$409$	−6.39927	−0.316424	−0.158212	+	0.987405i	$0.550573\pi$
$410$	−11.7493	−0.580255
$411$	−6.27249	−0.309399
$412$	−6.16248	−0.303604
$413$	−27.3798	−1.34727
$414$	−18.1369	−0.891382
$415$	−23.0750	−1.13270
$416$	−1.47624	−0.0723787
$417$	−4.79912	−0.235014
$418$	26.6588	1.30392
$419$	−1.83052	−0.0894268	−0.0447134	−	0.999000i	$-0.514237\pi$
$419$	−1.83052	−0.0894268	−0.0447134	+	0.999000i	$0.514237\pi$
$420$	−1.12165	−0.0547308
$421$	20.4495	0.996647	0.498323	−	0.866991i	$-0.333949\pi$
$421$	20.4495	0.996647	0.498323	+	0.866991i	$0.333949\pi$
$422$	14.2400	0.693194
$423$	15.1243	0.735368
$424$	−8.60020	−0.417663
$425$	−4.31920	−0.209512
$426$	−4.82812	−0.233923
$427$	−32.3295	−1.56453
$428$	0.356049	0.0172103
$429$	−2.32141	−0.112079
$430$	8.82723	0.425687
$431$	−33.3986	−1.60875	−0.804377	−	0.594120i	$-0.797500\pi$
$431$	−33.3986	−1.60875	−0.804377	+	0.594120i	$0.797500\pi$
$432$	1.71133	0.0823362
$433$	−8.10925	−0.389706	−0.194853	−	0.980832i	$-0.562423\pi$
$433$	−8.10925	−0.389706	−0.194853	+	0.980832i	$0.562423\pi$
$434$	2.57965	0.123827
$435$	2.48023	0.118918
$436$	10.4557	0.500736
$437$	−30.4967	−1.45886
$438$	2.61165	0.124789
$439$	9.33361	0.445469	0.222734	−	0.974879i	$-0.428502\pi$
$439$	9.33361	0.445469	0.222734	+	0.974879i	$0.428502\pi$
$440$	8.17202	0.389586
$441$	1.00732	0.0479674
$442$	−2.32673	−0.110671
$443$	−5.20996	−0.247533	−0.123766	−	0.992311i	$-0.539497\pi$
$443$	−5.20996	−0.247533	−0.123766	+	0.992311i	$0.539497\pi$
$444$	1.66032	0.0787955
$445$	22.9511	1.08799
$446$	−17.0203	−0.805935
$447$	−0.961946	−0.0454985
$448$	−2.57965	−0.121877
$449$	−6.33982	−0.299195	−0.149597	−	0.988747i	$-0.547798\pi$
$449$	−6.33982	−0.299195	−0.149597	+	0.988747i	$0.547798\pi$
$450$	7.99193	0.376743
$451$	−42.4922	−2.00088
$452$	3.47736	0.163561
$453$	4.59095	0.215702
$454$	12.7620	0.598951
$455$	−5.72445	−0.268366
$456$	1.41843	0.0664238
$457$	−21.5562	−1.00836	−0.504179	−	0.863599i	$-0.668205\pi$
$457$	−21.5562	−1.00836	−0.504179	+	0.863599i	$0.668205\pi$
$458$	14.1584	0.661579
$459$	2.69725	0.125897
$460$	−9.34852	−0.435877
$461$	23.5444	1.09657	0.548286	−	0.836291i	$-0.315281\pi$
$461$	23.5444	1.09657	0.548286	+	0.836291i	$0.315281\pi$
$462$	−4.05653	−0.188727
$463$	−12.5624	−0.583822	−0.291911	−	0.956445i	$-0.594291\pi$
$463$	−12.5624	−0.583822	−0.291911	+	0.956445i	$0.594291\pi$
$464$	5.70422	0.264812
$465$	−0.434806	−0.0201637
$466$	15.1467	0.701656
$467$	−26.8493	−1.24244	−0.621219	−	0.783637i	$-0.713362\pi$
$467$	−26.8493	−1.24244	−0.621219	+	0.783637i	$0.713362\pi$
$468$	4.30521	0.199009
$469$	17.7875	0.821349
$470$	7.79567	0.359587
$471$	2.46848	0.113742
$472$	10.6138	0.488538
$473$	31.9244	1.46789
$474$	0.564222	0.0259156
$475$	13.4382	0.616586
$476$	−4.06584	−0.186357
$477$	25.0810	1.14838
$478$	−19.3227	−0.883801
$479$	19.9778	0.912810	0.456405	−	0.889772i	$-0.349137\pi$
$479$	19.9778	0.912810	0.456405	+	0.889772i	$0.349137\pi$
$480$	0.434806	0.0198461
$481$	8.47365	0.386365
$482$	−7.59597	−0.345987
$483$	4.64054	0.211152
$484$	18.5548	0.843400
$485$	1.50320	0.0682566
$486$	−7.52148	−0.341181
$487$	40.2118	1.82217	0.911086	−	0.412216i	$-0.135245\pi$
$487$	40.2118	1.82217	0.911086	+	0.412216i	$0.135245\pi$
$488$	12.5325	0.567320
$489$	−3.69146	−0.166934
$490$	0.519212	0.0234556
$491$	15.6815	0.707697	0.353849	−	0.935303i	$-0.384873\pi$
$491$	15.6815	0.707697	0.353849	+	0.935303i	$0.384873\pi$
$492$	−2.26087	−0.101928
$493$	8.99053	0.404913
$494$	7.23909	0.325702
$495$	−23.8323	−1.07118
$496$	−1.00000	−0.0449013
$497$	−43.0585	−1.93144
$498$	−4.44023	−0.198972
$499$	23.1223	1.03510	0.517549	−	0.855654i	$-0.326845\pi$
$499$	23.1223	1.03510	0.517549	+	0.855654i	$0.326845\pi$
$500$	11.6353	0.520348
$501$	−1.44589	−0.0645978
$502$	−15.2888	−0.682374
$503$	6.30843	0.281279	0.140639	−	0.990061i	$-0.455084\pi$
$503$	6.30843	0.281279	0.140639	+	0.990061i	$0.455084\pi$
$504$	7.52312	0.335106
$505$	22.8832	1.01829
$506$	−33.8097	−1.50302
$507$	3.12994	0.139006
$508$	17.9293	0.795483
$509$	−3.78282	−0.167670	−0.0838352	−	0.996480i	$-0.526717\pi$
$509$	−3.78282	−0.167670	−0.0838352	+	0.996480i	$0.526717\pi$
$510$	0.685306	0.0303459
$511$	23.2914	1.03035
$512$	1.00000	0.0441942
$513$	−8.39187	−0.370510
$514$	3.84806	0.169731
$515$	9.26341	0.408195
$516$	1.69859	0.0747764
$517$	28.1937	1.23996
$518$	14.8072	0.650592
$519$	6.68803	0.293572
$520$	2.21908	0.0973131
$521$	−41.9959	−1.83987	−0.919937	−	0.392065i	$-0.871761\pi$
$521$	−41.9959	−1.83987	−0.919937	+	0.392065i	$0.871761\pi$
$522$	−16.6354	−0.728111
$523$	26.1002	1.14128	0.570642	−	0.821199i	$-0.306694\pi$
$523$	26.1002	1.14128	0.570642	+	0.821199i	$0.306694\pi$
$524$	14.9218	0.651863
$525$	−2.04482	−0.0892434
$526$	−23.9276	−1.04329
$527$	−1.57612	−0.0686568
$528$	1.57251	0.0684349
$529$	15.6772	0.681615
$530$	12.9278	0.561547
$531$	−30.9532	−1.34326
$532$	12.6499	0.548443
$533$	−11.5386	−0.499792
$534$	4.41640	0.191116
$535$	−0.535211	−0.0231392
$536$	−6.89530	−0.297832
$537$	−5.61257	−0.242200
$538$	−26.9454	−1.16170
$539$	1.87777	0.0808814
$540$	−2.57246	−0.110701
$541$	−10.5980	−0.455643	−0.227822	−	0.973703i	$-0.573160\pi$
$541$	−10.5980	−0.455643	−0.227822	+	0.973703i	$0.573160\pi$
$542$	23.3843	1.00444
$543$	2.13021	0.0914159
$544$	1.57612	0.0675755
$545$	−15.7169	−0.673239
$546$	−1.10154	−0.0471414
$547$	−34.0006	−1.45376	−0.726881	−	0.686763i	$-0.759031\pi$
$547$	−34.0006	−1.45376	−0.726881	+	0.686763i	$0.759031\pi$
$548$	21.6850	0.926338
$549$	−36.5490	−1.55987
$550$	14.8980	0.635254
$551$	−27.9719	−1.19164
$552$	−1.79890	−0.0765664
$553$	5.03188	0.213977
$554$	−14.2148	−0.603927
$555$	−2.49579	−0.105940
$556$	16.5913	0.703629
$557$	1.08791	0.0460960	0.0230480	−	0.999734i	$-0.492663\pi$
$557$	1.08791	0.0460960	0.0230480	+	0.999734i	$0.492663\pi$
$558$	2.91633	0.123458
$559$	8.66896	0.366658
$560$	3.87772	0.163863
$561$	2.47847	0.104641
$562$	−10.5957	−0.446953
$563$	−8.69617	−0.366500	−0.183250	−	0.983066i	$-0.558662\pi$
$563$	−8.69617	−0.366500	−0.183250	+	0.983066i	$0.558662\pi$
$564$	1.50009	0.0631653
$565$	−5.22715	−0.219908
$566$	−2.34298	−0.0984829
$567$	−21.2924	−0.894197
$568$	16.6916	0.700364
$569$	−20.1471	−0.844611	−0.422305	−	0.906454i	$-0.638779\pi$
$569$	−20.1471	−0.844611	−0.422305	+	0.906454i	$0.638779\pi$
$570$	−2.13217	−0.0893068
$571$	42.0224	1.75858	0.879291	−	0.476285i	$-0.158017\pi$
$571$	42.0224	1.75858	0.879291	+	0.476285i	$0.158017\pi$
$572$	8.02549	0.335563
$573$	5.30362	0.221562
$574$	−20.1630	−0.841589
$575$	−17.0428	−0.710735
$576$	−2.91633	−0.121514
$577$	46.4860	1.93524	0.967620	−	0.252413i	$-0.0812242\pi$
$577$	46.4860	1.93524	0.967620	+	0.252413i	$0.0812242\pi$
$578$	−14.5158	−0.603780
$579$	−0.823663	−0.0342303
$580$	−8.57455	−0.356039
$581$	−39.5992	−1.64285
$582$	0.289255	0.0119900
$583$	46.7544	1.93637
$584$	−9.02889	−0.373618
$585$	−6.47158	−0.267567
$586$	9.50205	0.392526
$587$	38.5401	1.59072	0.795360	−	0.606137i	$-0.207282\pi$
$587$	38.5401	1.59072	0.795360	+	0.606137i	$0.207282\pi$
$588$	0.0999101	0.00412022
$589$	4.90373	0.202054
$590$	−15.9545	−0.656838
$591$	−3.43274	−0.141204
$592$	−5.74001	−0.235913
$593$	8.86022	0.363846	0.181923	−	0.983313i	$-0.441768\pi$
$593$	8.86022	0.363846	0.181923	+	0.983313i	$0.441768\pi$
$594$	−9.30351	−0.381728
$595$	6.11175	0.250557
$596$	3.32560	0.136222
$597$	3.79108	0.155158
$598$	−9.18089	−0.375435
$599$	11.8729	0.485114	0.242557	−	0.970137i	$-0.422014\pi$
$599$	11.8729	0.485114	0.242557	+	0.970137i	$0.422014\pi$
$600$	0.792674	0.0323608
$601$	13.4142	0.547178	0.273589	−	0.961847i	$-0.411789\pi$
$601$	13.4142	0.547178	0.273589	+	0.961847i	$0.411789\pi$
$602$	15.1485	0.617407
$603$	20.1090	0.818901
$604$	−15.8717	−0.645809
$605$	−27.8915	−1.13395
$606$	4.40333	0.178873
$607$	0.903976	0.0366913	0.0183456	−	0.999832i	$-0.494160\pi$
$607$	0.903976	0.0366913	0.0183456	+	0.999832i	$0.494160\pi$
$608$	−4.90373	−0.198872
$609$	4.25635	0.172476
$610$	−18.8388	−0.762762
$611$	7.65589	0.309724
$612$	−4.59649	−0.185802
$613$	5.87406	0.237251	0.118626	−	0.992939i	$-0.462151\pi$
$613$	5.87406	0.237251	0.118626	+	0.992939i	$0.462151\pi$
$614$	10.0935	0.407339
$615$	3.39853	0.137042
$616$	14.0241	0.565047
$617$	−16.2500	−0.654201	−0.327101	−	0.944990i	$-0.606072\pi$
$617$	−16.2500	−0.654201	−0.327101	+	0.944990i	$0.606072\pi$
$618$	1.78253	0.0717037
$619$	−36.0117	−1.44743	−0.723717	−	0.690097i	$-0.757568\pi$
$619$	−36.0117	−1.44743	−0.723717	+	0.690097i	$0.757568\pi$
$620$	1.50320	0.0603698
$621$	10.6429	0.427085
$622$	26.7523	1.07267
$623$	39.3866	1.57799
$624$	0.427010	0.0170941
$625$	−3.78817	−0.151527
$626$	16.1257	0.644511
$627$	−7.71117	−0.307955
$628$	−8.53394	−0.340541
$629$	−9.04694	−0.360725
$630$	−11.3087	−0.450550
$631$	29.4146	1.17098	0.585489	−	0.810680i	$-0.300902\pi$
$631$	29.4146	1.17098	0.585489	+	0.810680i	$0.300902\pi$
$632$	−1.95061	−0.0775910
$633$	−4.11900	−0.163715
$634$	0.604638	0.0240132
$635$	−26.9512	−1.06953
$636$	2.48765	0.0986416
$637$	0.509902	0.0202030
$638$	−31.0106	−1.22772
$639$	−48.6782	−1.92568
$640$	−1.50320	−0.0594190
$641$	16.3533	0.645917	0.322958	−	0.946413i	$-0.395323\pi$
$641$	16.3533	0.645917	0.322958	+	0.946413i	$0.395323\pi$
$642$	−0.102989	−0.00406464
$643$	22.2686	0.878189	0.439094	−	0.898441i	$-0.355299\pi$
$643$	22.2686	0.878189	0.439094	+	0.898441i	$0.355299\pi$
$644$	−16.0431	−0.632186
$645$	−2.55332	−0.100537
$646$	−7.72885	−0.304088
$647$	37.2193	1.46324	0.731620	−	0.681713i	$-0.238765\pi$
$647$	37.2193	1.46324	0.731620	+	0.681713i	$0.238765\pi$
$648$	8.25399	0.324247
$649$	−57.7010	−2.26496
$650$	4.04550	0.158678
$651$	−0.746176	−0.0292449
$652$	12.7620	0.499798
$653$	−24.0797	−0.942313	−0.471156	−	0.882050i	$-0.656163\pi$
$653$	−24.0797	−0.942313	−0.471156	+	0.882050i	$0.656163\pi$
$654$	−3.02435	−0.118262
$655$	−22.4304	−0.876428
$656$	7.81619	0.305171
$657$	26.3312	1.02728
$658$	13.3782	0.521538
$659$	−16.0484	−0.625158	−0.312579	−	0.949892i	$-0.601193\pi$
$659$	−16.0484	−0.625158	−0.312579	+	0.949892i	$0.601193\pi$
$660$	−2.36379	−0.0920106
$661$	−11.4098	−0.443789	−0.221895	−	0.975071i	$-0.571224\pi$
$661$	−11.4098	−0.443789	−0.221895	+	0.975071i	$0.571224\pi$
$662$	15.3115	0.595100
$663$	0.673018	0.0261379
$664$	15.3506	0.595719
$665$	−19.0153	−0.737380
$666$	16.7398	0.648653
$667$	35.4751	1.37360
$668$	4.99869	0.193405
$669$	4.92320	0.190342
$670$	10.3650	0.400434
$671$	−68.1322	−2.63021
$672$	0.746176	0.0287844
$673$	−47.0193	−1.81246	−0.906230	−	0.422785i	$-0.861052\pi$
$673$	−47.0193	−1.81246	−0.906230	+	0.422785i	$0.861052\pi$
$674$	10.0245	0.386128
$675$	−4.68973	−0.180508
$676$	−10.8207	−0.416181
$677$	38.4263	1.47684	0.738421	−	0.674340i	$-0.235572\pi$
$677$	38.4263	1.47684	0.738421	+	0.674340i	$0.235572\pi$
$678$	−1.00584	−0.0386291
$679$	2.57965	0.0989979
$680$	−2.36921	−0.0908552
$681$	−3.69147	−0.141458
$682$	5.43643	0.208172
$683$	20.6342	0.789546	0.394773	−	0.918779i	$-0.370823\pi$
$683$	20.6342	0.789546	0.394773	+	0.918779i	$0.370823\pi$
$684$	14.3009	0.546808
$685$	−32.5968	−1.24546
$686$	18.9486	0.723460
$687$	−4.09538	−0.156249
$688$	−5.87231	−0.223880
$689$	12.6960	0.483678
$690$	2.70410	0.102943
$691$	44.3693	1.68789	0.843943	−	0.536432i	$-0.180228\pi$
$691$	44.3693	1.68789	0.843943	+	0.536432i	$0.180228\pi$
$692$	−23.1216	−0.878952
$693$	−40.8989	−1.55362
$694$	−2.36918	−0.0899328
$695$	−24.9400	−0.946028
$696$	−1.64997	−0.0625420
$697$	12.3193	0.466625
$698$	19.2788	0.729714
$699$	−4.38125	−0.165714
$700$	7.06928	0.267194
$701$	8.19284	0.309439	0.154720	−	0.987958i	$-0.450553\pi$
$701$	8.19284	0.309439	0.154720	+	0.987958i	$0.450553\pi$
$702$	−2.52633	−0.0953503
$703$	28.1474	1.06160
$704$	−5.43643	−0.204893
$705$	−2.25493	−0.0849257
$706$	−22.5343	−0.848091
$707$	39.2700	1.47690
$708$	−3.07008	−0.115381
$709$	25.8340	0.970215	0.485107	−	0.874455i	$-0.338781\pi$
$709$	25.8340	0.970215	0.485107	+	0.874455i	$0.338781\pi$
$710$	−25.0907	−0.941638
$711$	5.68862	0.213340
$712$	−15.2682	−0.572200
$713$	−6.21910	−0.232907
$714$	1.17606	0.0440130
$715$	−12.0639	−0.451164
$716$	19.4036	0.725145
$717$	5.58919	0.208732
$718$	−0.258059	−0.00963066
$719$	−23.4154	−0.873245	−0.436623	−	0.899645i	$-0.643825\pi$
$719$	−23.4154	−0.873245	−0.436623	+	0.899645i	$0.643825\pi$
$720$	4.38382	0.163375
$721$	15.8970	0.592037
$722$	5.04652	0.187812
$723$	2.19717	0.0817136
$724$	−7.36447	−0.273698
$725$	−15.6319	−0.580553
$726$	−5.36706	−0.199190
$727$	35.2228	1.30634	0.653171	−	0.757210i	$-0.273438\pi$
$727$	35.2228	1.30634	0.653171	+	0.757210i	$0.273438\pi$
$728$	3.80819	0.141141
$729$	−22.5863	−0.836531
$730$	13.5722	0.502329
$731$	−9.25546	−0.342326
$732$	−3.62509	−0.133987
$733$	−18.5217	−0.684113	−0.342057	−	0.939679i	$-0.611123\pi$
$733$	−18.5217	−0.684113	−0.342057	+	0.939679i	$0.611123\pi$
$734$	−35.9593	−1.32728
$735$	−0.150184	−0.00553963
$736$	6.21910	0.229239
$737$	37.4858	1.38081
$738$	−22.7946	−0.839081
$739$	34.6748	1.27553	0.637767	−	0.770229i	$-0.279858\pi$
$739$	34.6748	1.27553	0.637767	+	0.770229i	$0.279858\pi$
$740$	8.62836	0.317185
$741$	−2.09394	−0.0769228
$742$	22.1855	0.814456
$743$	31.3124	1.14874	0.574371	−	0.818595i	$-0.305247\pi$
$743$	31.3124	1.14874	0.574371	+	0.818595i	$0.305247\pi$
$744$	0.289255	0.0106046
$745$	−4.99903	−0.183150
$746$	28.4290	1.04086
$747$	−44.7674	−1.63796
$748$	−8.56847	−0.313294
$749$	−0.918481	−0.0335606
$750$	−3.36558	−0.122893
$751$	−45.0869	−1.64524	−0.822621	−	0.568589i	$-0.807489\pi$
$751$	−45.0869	−1.64524	−0.822621	+	0.568589i	$0.807489\pi$
$752$	−5.18606	−0.189116
$753$	4.42237	0.161160
$754$	−8.42081	−0.306668
$755$	23.8582	0.868290
$756$	−4.41462	−0.160558
$757$	17.6092	0.640017	0.320009	−	0.947415i	$-0.396314\pi$
$757$	17.6092	0.640017	0.320009	+	0.947415i	$0.396314\pi$
$758$	5.01658	0.182210
$759$	9.77961	0.354977
$760$	7.37126	0.267384
$761$	−29.5554	−1.07138	−0.535691	−	0.844414i	$-0.679949\pi$
$761$	−29.5554	−1.07138	−0.535691	+	0.844414i	$0.679949\pi$
$762$	−5.18613	−0.187874
$763$	−26.9720	−0.976451
$764$	−18.3355	−0.663353
$765$	6.90942	0.249810
$766$	−0.233452	−0.00843498
$767$	−15.6685	−0.565756
$768$	−0.289255	−0.0104376
$769$	10.6173	0.382868	0.191434	−	0.981505i	$-0.438686\pi$
$769$	10.6173	0.382868	0.191434	+	0.981505i	$0.438686\pi$
$770$	−21.0810	−0.759705
$771$	−1.11307	−0.0400862
$772$	2.84754	0.102485
$773$	5.25638	0.189059	0.0945295	−	0.995522i	$-0.469865\pi$
$773$	5.25638	0.189059	0.0945295	+	0.995522i	$0.469865\pi$
$774$	17.1256	0.615567
$775$	2.74040	0.0984382
$776$	−1.00000	−0.0358979
$777$	−4.28306	−0.153654
$778$	−10.9885	−0.393957
$779$	−38.3285	−1.37326
$780$	−0.641879	−0.0229830
$781$	−90.7427	−3.24703
$782$	9.80204	0.350520
$783$	9.76178	0.348857
$784$	−0.345405	−0.0123359
$785$	12.8282	0.457857
$786$	−4.31620	−0.153954
$787$	9.23729	0.329274	0.164637	−	0.986354i	$-0.447355\pi$
$787$	9.23729	0.329274	0.164637	+	0.986354i	$0.447355\pi$
$788$	11.8675	0.422763
$789$	6.92116	0.246400
$790$	2.93214	0.104321
$791$	−8.97037	−0.318950
$792$	15.8544	0.563363
$793$	−18.5010	−0.656991
$794$	21.7365	0.771398
$795$	−3.73942	−0.132624
$796$	−13.1064	−0.464543
$797$	−9.52465	−0.337380	−0.168690	−	0.985669i	$-0.553954\pi$
$797$	−9.52465	−0.337380	−0.168690	+	0.985669i	$0.553954\pi$
$798$	−3.65904	−0.129529
$799$	−8.17385	−0.289170
$800$	−2.74040	−0.0968879
$801$	44.5272	1.57329
$802$	−30.5399	−1.07840
$803$	49.0850	1.73217
$804$	1.99450	0.0703405
$805$	24.1159	0.849974
$806$	1.47624	0.0519984
$807$	7.79409	0.274365
$808$	−15.2230	−0.535544
$809$	48.4219	1.70242	0.851212	−	0.524823i	$-0.175868\pi$
$809$	48.4219	1.70242	0.851212	+	0.524823i	$0.175868\pi$
$810$	−12.4074	−0.435950
$811$	−34.8630	−1.22421	−0.612103	−	0.790778i	$-0.709676\pi$
$811$	−34.8630	−1.22421	−0.612103	+	0.790778i	$0.709676\pi$
$812$	−14.7149	−0.516391
$813$	−6.76402	−0.237224
$814$	31.2052	1.09374
$815$	−19.1837	−0.671977
$816$	−0.455900	−0.0159597
$817$	28.7962	1.00745
$818$	−6.39927	−0.223745
$819$	−11.1059	−0.388073
$820$	−11.7493	−0.410302
$821$	6.79165	0.237030	0.118515	−	0.992952i	$-0.462187\pi$
$821$	6.79165	0.237030	0.118515	+	0.992952i	$0.462187\pi$
$822$	−6.27249	−0.218778
$823$	6.22217	0.216891	0.108446	−	0.994102i	$-0.465413\pi$
$823$	6.22217	0.216891	0.108446	+	0.994102i	$0.465413\pi$
$824$	−6.16248	−0.214680
$825$	−4.30932	−0.150031
$826$	−27.3798	−0.952664
$827$	−34.8208	−1.21084	−0.605418	−	0.795907i	$-0.706994\pi$
$827$	−34.8208	−1.21084	−0.605418	+	0.795907i	$0.706994\pi$
$828$	−18.1369	−0.630302
$829$	−44.9260	−1.56034	−0.780172	−	0.625565i	$-0.784868\pi$
$829$	−44.9260	−1.56034	−0.780172	+	0.625565i	$0.784868\pi$
$830$	−23.0750	−0.800943
$831$	4.11169	0.142633
$832$	−1.47624	−0.0511795
$833$	−0.544400	−0.0188623
$834$	−4.79912	−0.166180
$835$	−7.51401	−0.260033
$836$	26.6588	0.922013
$837$	−1.71133	−0.0591521
$838$	−1.83052	−0.0632343
$839$	−0.488921	−0.0168794	−0.00843972	−	0.999964i	$-0.502686\pi$
$839$	−0.488921	−0.0168794	−0.00843972	+	0.999964i	$0.502686\pi$
$840$	−1.12165	−0.0387005
$841$	3.53810	0.122004
$842$	20.4495	0.704736
$843$	3.06486	0.105559
$844$	14.2400	0.490162
$845$	16.2656	0.559555
$846$	15.1243	0.519983
$847$	−47.8649	−1.64466
$848$	−8.60020	−0.295332
$849$	0.677718	0.0232592
$850$	−4.31920	−0.148147
$851$	−35.6977	−1.22370
$852$	−4.82812	−0.165409
$853$	18.8008	0.643726	0.321863	−	0.946786i	$-0.395691\pi$
$853$	18.8008	0.643726	0.321863	+	0.946786i	$0.395691\pi$
$854$	−32.3295	−1.10629
$855$	−21.4970	−0.735183
$856$	0.356049	0.0121695
$857$	26.9176	0.919489	0.459745	−	0.888051i	$-0.347941\pi$
$857$	26.9176	0.919489	0.459745	+	0.888051i	$0.347941\pi$
$858$	−2.32141	−0.0792517
$859$	−2.55378	−0.0871337	−0.0435668	−	0.999051i	$-0.513872\pi$
$859$	−2.55378	−0.0871337	−0.0435668	+	0.999051i	$0.513872\pi$
$860$	8.82723	0.301006
$861$	5.83225	0.198763
$862$	−33.3986	−1.13756
$863$	9.26102	0.315249	0.157624	−	0.987499i	$-0.449616\pi$
$863$	9.26102	0.315249	0.157624	+	0.987499i	$0.449616\pi$
$864$	1.71133	0.0582205
$865$	34.7563	1.18175
$866$	−8.10925	−0.275563
$867$	4.19878	0.142598
$868$	2.57965	0.0875590
$869$	10.6043	0.359728
$870$	2.48023	0.0840876
$871$	10.1791	0.344907
$872$	10.4557	0.354074
$873$	2.91633	0.0987029
$874$	−30.4967	−1.03157
$875$	−30.0151	−1.01470
$876$	2.61165	0.0882395
$877$	−0.626320	−0.0211493	−0.0105747	−	0.999944i	$-0.503366\pi$
$877$	−0.626320	−0.0211493	−0.0105747	+	0.999944i	$0.503366\pi$
$878$	9.33361	0.314994
$879$	−2.74851	−0.0927050
$880$	8.17202	0.275479
$881$	34.2822	1.15500	0.577498	−	0.816392i	$-0.304029\pi$
$881$	34.2822	1.15500	0.577498	+	0.816392i	$0.304029\pi$
$882$	1.00732	0.0339181
$883$	−21.7602	−0.732289	−0.366145	−	0.930558i	$-0.619322\pi$
$883$	−21.7602	−0.732289	−0.366145	+	0.930558i	$0.619322\pi$
$884$	−2.32673	−0.0782565
$885$	4.61493	0.155129
$886$	−5.20996	−0.175032
$887$	−3.87895	−0.130243	−0.0651213	−	0.997877i	$-0.520743\pi$
$887$	−3.87895	−0.130243	−0.0651213	+	0.997877i	$0.520743\pi$
$888$	1.66032	0.0557169
$889$	−46.2513	−1.55122
$890$	22.9511	0.769323
$891$	−44.8722	−1.50328
$892$	−17.0203	−0.569882
$893$	25.4310	0.851017
$894$	−0.961946	−0.0321723
$895$	−29.1673	−0.974957
$896$	−2.57965	−0.0861801
$897$	2.65562	0.0886684
$898$	−6.33982	−0.211563
$899$	−5.70422	−0.190246
$900$	7.99193	0.266398
$901$	−13.5549	−0.451580
$902$	−42.4922	−1.41484
$903$	−4.38178	−0.145816
$904$	3.47736	0.115655
$905$	11.0702	0.367987
$906$	4.59095	0.152524
$907$	−40.0130	−1.32861	−0.664305	−	0.747462i	$-0.731272\pi$
$907$	−40.0130	−1.32861	−0.664305	+	0.747462i	$0.731272\pi$
$908$	12.7620	0.423522
$909$	44.3954	1.47250
$910$	−5.72445	−0.189764
$911$	−50.0007	−1.65660	−0.828299	−	0.560287i	$-0.810691\pi$
$911$	−50.0007	−1.65660	−0.828299	+	0.560287i	$0.810691\pi$
$912$	1.41843	0.0469688
$913$	−83.4525	−2.76188
$914$	−21.5562	−0.713017
$915$	5.44922	0.180146
$916$	14.1584	0.467807
$917$	−38.4931	−1.27115
$918$	2.69725	0.0890226
$919$	−41.8559	−1.38070	−0.690349	−	0.723476i	$-0.742543\pi$
$919$	−41.8559	−1.38070	−0.690349	+	0.723476i	$0.742543\pi$
$920$	−9.34852	−0.308211
$921$	−2.91958	−0.0962034
$922$	23.5444	0.775393
$923$	−24.6408	−0.811063
$924$	−4.05653	−0.133450
$925$	15.7299	0.517198
$926$	−12.5624	−0.412825
$927$	17.9718	0.590272
$928$	5.70422	0.187250
$929$	42.2700	1.38683	0.693417	−	0.720536i	$-0.256104\pi$
$929$	42.2700	1.38683	0.693417	+	0.720536i	$0.256104\pi$
$930$	−0.434806	−0.0142579
$931$	1.69377	0.0555111
$932$	15.1467	0.496146
$933$	−7.73824	−0.253339
$934$	−26.8493	−0.878536
$935$	12.8801	0.421224
$936$	4.30521	0.140720
$937$	−16.0397	−0.523995	−0.261997	−	0.965069i	$-0.584381\pi$
$937$	−16.0397	−0.523995	−0.261997	+	0.965069i	$0.584381\pi$
$938$	17.7875	0.580781
$939$	−4.66442	−0.152218
$940$	7.79567	0.254267
$941$	50.8166	1.65657	0.828287	−	0.560303i	$-0.189315\pi$
$941$	50.8166	1.65657	0.828287	+	0.560303i	$0.189315\pi$
$942$	2.46848	0.0804275
$943$	48.6097	1.58295
$944$	10.6138	0.345448
$945$	6.63604	0.215870
$946$	31.9244	1.03795
$947$	−45.9528	−1.49327	−0.746633	−	0.665237i	$-0.768331\pi$
$947$	−45.9528	−1.49327	−0.746633	+	0.665237i	$0.768331\pi$
$948$	0.564222	0.0183251
$949$	13.3288	0.432672
$950$	13.4382	0.435992
$951$	−0.174894	−0.00567134
$952$	−4.06584	−0.131774
$953$	−37.4773	−1.21401	−0.607004	−	0.794698i	$-0.707629\pi$
$953$	−37.4773	−1.21401	−0.607004	+	0.794698i	$0.707629\pi$
$954$	25.0810	0.812028
$955$	27.5618	0.891878
$956$	−19.3227	−0.624942
$957$	8.96996	0.289958
$958$	19.9778	0.645454
$959$	−55.9397	−1.80639
$960$	0.434806	0.0140333
$961$	1.00000	0.0322581
$962$	8.47365	0.273201
$963$	−1.03836	−0.0334606
$964$	−7.59597	−0.244650
$965$	−4.28041	−0.137791
$966$	4.64054	0.149307
$967$	−44.5667	−1.43317	−0.716585	−	0.697500i	$-0.754296\pi$
$967$	−44.5667	−1.43317	−0.716585	+	0.697500i	$0.754296\pi$
$968$	18.5548	0.596374
$969$	2.23561	0.0718180
$970$	1.50320	0.0482647
$971$	2.62249	0.0841596	0.0420798	−	0.999114i	$-0.486602\pi$
$971$	2.62249	0.0841596	0.0420798	+	0.999114i	$0.486602\pi$
$972$	−7.52148	−0.241252
$973$	−42.7998	−1.37210
$974$	40.2118	1.28847
$975$	−1.17018	−0.0374757
$976$	12.5325	0.401156
$977$	47.5295	1.52060	0.760301	−	0.649570i	$-0.225051\pi$
$977$	47.5295	1.52060	0.760301	+	0.649570i	$0.225051\pi$
$978$	−3.69146	−0.118040
$979$	83.0046	2.65284
$980$	0.519212	0.0165856
$981$	−30.4922	−0.973541
$982$	15.6815	0.500417
$983$	−21.9104	−0.698834	−0.349417	−	0.936967i	$-0.613620\pi$
$983$	−21.9104	−0.698834	−0.349417	+	0.936967i	$0.613620\pi$
$984$	−2.26087	−0.0720739
$985$	−17.8392	−0.568404
$986$	8.99053	0.286317
$987$	−3.86971	−0.123174
$988$	7.23909	0.230306
$989$	−36.5205	−1.16128
$990$	−23.8323	−0.757441
$991$	−16.9433	−0.538221	−0.269110	−	0.963109i	$-0.586730\pi$
$991$	−16.9433	−0.538221	−0.269110	+	0.963109i	$0.586730\pi$
$992$	−1.00000	−0.0317500
$993$	−4.42893	−0.140548
$994$	−43.0585	−1.36573
$995$	19.7014	0.624577
$996$	−4.44023	−0.140694
$997$	2.00466	0.0634881	0.0317440	−	0.999496i	$-0.489894\pi$
$997$	2.00466	0.0634881	0.0317440	+	0.999496i	$0.489894\pi$
$998$	23.1223	0.731925
$999$	−9.82303	−0.310787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.13	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.13	✓	28	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.289255 q^{3} +1.00000 q^{4} -1.50320 q^{5} -0.289255 q^{6} -2.57965 q^{7} +1.00000 q^{8} -2.91633 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.289255 q^{3} +1.00000 q^{4} -1.50320 q^{5} -0.289255 q^{6} -2.57965 q^{7} +1.00000 q^{8} -2.91633 q^{9} -1.50320 q^{10} -5.43643 q^{11} -0.289255 q^{12} -1.47624 q^{13} -2.57965 q^{14} +0.434806 q^{15} +1.00000 q^{16} +1.57612 q^{17} -2.91633 q^{18} -4.90373 q^{19} -1.50320 q^{20} +0.746176 q^{21} -5.43643 q^{22} +6.21910 q^{23} -0.289255 q^{24} -2.74040 q^{25} -1.47624 q^{26} +1.71133 q^{27} -2.57965 q^{28} +5.70422 q^{29} +0.434806 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.57251 q^{33} +1.57612 q^{34} +3.87772 q^{35} -2.91633 q^{36} -5.74001 q^{37} -4.90373 q^{38} +0.427010 q^{39} -1.50320 q^{40} +7.81619 q^{41} +0.746176 q^{42} -5.87231 q^{43} -5.43643 q^{44} +4.38382 q^{45} +6.21910 q^{46} -5.18606 q^{47} -0.289255 q^{48} -0.345405 q^{49} -2.74040 q^{50} -0.455900 q^{51} -1.47624 q^{52} -8.60020 q^{53} +1.71133 q^{54} +8.17202 q^{55} -2.57965 q^{56} +1.41843 q^{57} +5.70422 q^{58} +10.6138 q^{59} +0.434806 q^{60} +12.5325 q^{61} -1.00000 q^{62} +7.52312 q^{63} +1.00000 q^{64} +2.21908 q^{65} +1.57251 q^{66} -6.89530 q^{67} +1.57612 q^{68} -1.79890 q^{69} +3.87772 q^{70} +16.6916 q^{71} -2.91633 q^{72} -9.02889 q^{73} -5.74001 q^{74} +0.792674 q^{75} -4.90373 q^{76} +14.0241 q^{77} +0.427010 q^{78} -1.95061 q^{79} -1.50320 q^{80} +8.25399 q^{81} +7.81619 q^{82} +15.3506 q^{83} +0.746176 q^{84} -2.36921 q^{85} -5.87231 q^{86} -1.64997 q^{87} -5.43643 q^{88} -15.2682 q^{89} +4.38382 q^{90} +3.80819 q^{91} +6.21910 q^{92} +0.289255 q^{93} -5.18606 q^{94} +7.37126 q^{95} -0.289255 q^{96} -1.00000 q^{97} -0.345405 q^{98} +15.8544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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