LMFDB - Embedded newform 6010.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.98091 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98091 q^{6} -1.31383 q^{7} +1.00000 q^{8} +0.924017 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.98091 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98091 q^{6} -1.31383 q^{7} +1.00000 q^{8} +0.924017 q^{9} -1.00000 q^{10} -3.29852 q^{11} -1.98091 q^{12} -2.77825 q^{13} -1.31383 q^{14} +1.98091 q^{15} +1.00000 q^{16} +5.53135 q^{17} +0.924017 q^{18} +8.26118 q^{19} -1.00000 q^{20} +2.60258 q^{21} -3.29852 q^{22} -3.94199 q^{23} -1.98091 q^{24} +1.00000 q^{25} -2.77825 q^{26} +4.11234 q^{27} -1.31383 q^{28} -10.2565 q^{29} +1.98091 q^{30} +8.12629 q^{31} +1.00000 q^{32} +6.53408 q^{33} +5.53135 q^{34} +1.31383 q^{35} +0.924017 q^{36} +3.13061 q^{37} +8.26118 q^{38} +5.50347 q^{39} -1.00000 q^{40} +6.16623 q^{41} +2.60258 q^{42} +7.50345 q^{43} -3.29852 q^{44} -0.924017 q^{45} -3.94199 q^{46} -2.19753 q^{47} -1.98091 q^{48} -5.27385 q^{49} +1.00000 q^{50} -10.9571 q^{51} -2.77825 q^{52} +1.42034 q^{53} +4.11234 q^{54} +3.29852 q^{55} -1.31383 q^{56} -16.3647 q^{57} -10.2565 q^{58} -13.2437 q^{59} +1.98091 q^{60} +7.06768 q^{61} +8.12629 q^{62} -1.21400 q^{63} +1.00000 q^{64} +2.77825 q^{65} +6.53408 q^{66} -7.92121 q^{67} +5.53135 q^{68} +7.80874 q^{69} +1.31383 q^{70} +1.57382 q^{71} +0.924017 q^{72} +7.48531 q^{73} +3.13061 q^{74} -1.98091 q^{75} +8.26118 q^{76} +4.33369 q^{77} +5.50347 q^{78} -8.41541 q^{79} -1.00000 q^{80} -10.9182 q^{81} +6.16623 q^{82} -1.48595 q^{83} +2.60258 q^{84} -5.53135 q^{85} +7.50345 q^{86} +20.3172 q^{87} -3.29852 q^{88} -3.59741 q^{89} -0.924017 q^{90} +3.65015 q^{91} -3.94199 q^{92} -16.0975 q^{93} -2.19753 q^{94} -8.26118 q^{95} -1.98091 q^{96} -4.31152 q^{97} -5.27385 q^{98} -3.04789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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
$3$	−1.98091	−1.14368	−0.571840	−	0.820365i	$-0.693770\pi$
$3$	−1.98091	−1.14368	−0.571840	+	0.820365i	$0.693770\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.98091	−0.808704
$7$	−1.31383	−0.496581	−0.248290	−	0.968686i	$-0.579869\pi$
$7$	−1.31383	−0.496581	−0.248290	+	0.968686i	$0.579869\pi$
$8$	1.00000	0.353553
$9$	0.924017	0.308006
$10$	−1.00000	−0.316228
$11$	−3.29852	−0.994541	−0.497271	−	0.867595i	$-0.665664\pi$
$11$	−3.29852	−0.994541	−0.497271	+	0.867595i	$0.665664\pi$
$12$	−1.98091	−0.571840
$13$	−2.77825	−0.770548	−0.385274	−	0.922802i	$-0.625893\pi$
$13$	−2.77825	−0.770548	−0.385274	+	0.922802i	$0.625893\pi$
$14$	−1.31383	−0.351136
$15$	1.98091	0.511470
$16$	1.00000	0.250000
$17$	5.53135	1.34155	0.670775	−	0.741661i	$-0.265962\pi$
$17$	5.53135	1.34155	0.670775	+	0.741661i	$0.265962\pi$
$18$	0.924017	0.217793
$19$	8.26118	1.89524	0.947622	−	0.319393i	$-0.103479\pi$
$19$	8.26118	1.89524	0.947622	+	0.319393i	$0.103479\pi$
$20$	−1.00000	−0.223607
$21$	2.60258	0.567930
$22$	−3.29852	−0.703247
$23$	−3.94199	−0.821962	−0.410981	−	0.911644i	$-0.634814\pi$
$23$	−3.94199	−0.821962	−0.410981	+	0.911644i	$0.634814\pi$
$24$	−1.98091	−0.404352
$25$	1.00000	0.200000
$26$	−2.77825	−0.544860
$27$	4.11234	0.791421
$28$	−1.31383	−0.248290
$29$	−10.2565	−1.90458	−0.952288	−	0.305200i	$-0.901277\pi$
$29$	−10.2565	−1.90458	−0.952288	+	0.305200i	$0.901277\pi$
$30$	1.98091	0.361664
$31$	8.12629	1.45953	0.729763	−	0.683700i	$-0.239631\pi$
$31$	8.12629	1.45953	0.729763	+	0.683700i	$0.239631\pi$
$32$	1.00000	0.176777
$33$	6.53408	1.13744
$34$	5.53135	0.948619
$35$	1.31383	0.222078
$36$	0.924017	0.154003
$37$	3.13061	0.514670	0.257335	−	0.966322i	$-0.417156\pi$
$37$	3.13061	0.514670	0.257335	+	0.966322i	$0.417156\pi$
$38$	8.26118	1.34014
$39$	5.50347	0.881261
$40$	−1.00000	−0.158114
$41$	6.16623	0.963003	0.481502	−	0.876445i	$-0.340092\pi$
$41$	6.16623	0.963003	0.481502	+	0.876445i	$0.340092\pi$
$42$	2.60258	0.401587
$43$	7.50345	1.14427	0.572133	−	0.820161i	$-0.306116\pi$
$43$	7.50345	1.14427	0.572133	+	0.820161i	$0.306116\pi$
$44$	−3.29852	−0.497271
$45$	−0.924017	−0.137744
$46$	−3.94199	−0.581215
$47$	−2.19753	−0.320543	−0.160271	−	0.987073i	$-0.551237\pi$
$47$	−2.19753	−0.320543	−0.160271	+	0.987073i	$0.551237\pi$
$48$	−1.98091	−0.285920
$49$	−5.27385	−0.753407
$50$	1.00000	0.141421
$51$	−10.9571	−1.53430
$52$	−2.77825	−0.385274
$53$	1.42034	0.195099	0.0975494	−	0.995231i	$-0.468900\pi$
$53$	1.42034	0.195099	0.0975494	+	0.995231i	$0.468900\pi$
$54$	4.11234	0.559619
$55$	3.29852	0.444772
$56$	−1.31383	−0.175568
$57$	−16.3647	−2.16755
$58$	−10.2565	−1.34674
$59$	−13.2437	−1.72419	−0.862093	−	0.506750i	$-0.830847\pi$
$59$	−13.2437	−1.72419	−0.862093	+	0.506750i	$0.830847\pi$
$60$	1.98091	0.255735
$61$	7.06768	0.904924	0.452462	−	0.891784i	$-0.350546\pi$
$61$	7.06768	0.904924	0.452462	+	0.891784i	$0.350546\pi$
$62$	8.12629	1.03204
$63$	−1.21400	−0.152950
$64$	1.00000	0.125000
$65$	2.77825	0.344600
$66$	6.53408	0.804290
$67$	−7.92121	−0.967730	−0.483865	−	0.875143i	$-0.660767\pi$
$67$	−7.92121	−0.967730	−0.483865	+	0.875143i	$0.660767\pi$
$68$	5.53135	0.670775
$69$	7.80874	0.940062
$70$	1.31383	0.157033
$71$	1.57382	0.186778	0.0933888	−	0.995630i	$-0.470230\pi$
$71$	1.57382	0.186778	0.0933888	+	0.995630i	$0.470230\pi$
$72$	0.924017	0.108896
$73$	7.48531	0.876089	0.438044	−	0.898953i	$-0.355671\pi$
$73$	7.48531	0.876089	0.438044	+	0.898953i	$0.355671\pi$
$74$	3.13061	0.363926
$75$	−1.98091	−0.228736
$76$	8.26118	0.947622
$77$	4.33369	0.493870
$78$	5.50347	0.623146
$79$	−8.41541	−0.946808	−0.473404	−	0.880845i	$-0.656975\pi$
$79$	−8.41541	−0.946808	−0.473404	+	0.880845i	$0.656975\pi$
$80$	−1.00000	−0.111803
$81$	−10.9182	−1.21314
$82$	6.16623	0.680946
$83$	−1.48595	−0.163104	−0.0815521	−	0.996669i	$-0.525988\pi$
$83$	−1.48595	−0.163104	−0.0815521	+	0.996669i	$0.525988\pi$
$84$	2.60258	0.283965
$85$	−5.53135	−0.599959
$86$	7.50345	0.809118
$87$	20.3172	2.17823
$88$	−3.29852	−0.351624
$89$	−3.59741	−0.381325	−0.190662	−	0.981656i	$-0.561064\pi$
$89$	−3.59741	−0.381325	−0.190662	+	0.981656i	$0.561064\pi$
$90$	−0.924017	−0.0973999
$91$	3.65015	0.382639
$92$	−3.94199	−0.410981
$93$	−16.0975	−1.66923
$94$	−2.19753	−0.226658
$95$	−8.26118	−0.847579
$96$	−1.98091	−0.202176
$97$	−4.31152	−0.437769	−0.218884	−	0.975751i	$-0.570242\pi$
$97$	−4.31152	−0.437769	−0.218884	+	0.975751i	$0.570242\pi$
$98$	−5.27385	−0.532740
$99$	−3.04789	−0.306324
$100$	1.00000	0.100000
$101$	−3.55203	−0.353440	−0.176720	−	0.984261i	$-0.556549\pi$
$101$	−3.55203	−0.353440	−0.176720	+	0.984261i	$0.556549\pi$
$102$	−10.9571	−1.08492
$103$	−14.9301	−1.47111	−0.735554	−	0.677466i	$-0.763078\pi$
$103$	−14.9301	−1.47111	−0.735554	+	0.677466i	$0.763078\pi$
$104$	−2.77825	−0.272430
$105$	−2.60258	−0.253986
$106$	1.42034	0.137956
$107$	−13.8993	−1.34370	−0.671848	−	0.740689i	$-0.734499\pi$
$107$	−13.8993	−1.34370	−0.671848	+	0.740689i	$0.734499\pi$
$108$	4.11234	0.395710
$109$	13.6002	1.30266	0.651332	−	0.758793i	$-0.274211\pi$
$109$	13.6002	1.30266	0.651332	+	0.758793i	$0.274211\pi$
$110$	3.29852	0.314502
$111$	−6.20147	−0.588618
$112$	−1.31383	−0.124145
$113$	−12.5287	−1.17860	−0.589300	−	0.807914i	$-0.700597\pi$
$113$	−12.5287	−1.17860	−0.589300	+	0.807914i	$0.700597\pi$
$114$	−16.3647	−1.53269
$115$	3.94199	0.367593
$116$	−10.2565	−0.952288
$117$	−2.56715	−0.237333
$118$	−13.2437	−1.21918
$119$	−7.26725	−0.666188
$120$	1.98091	0.180832
$121$	−0.119759	−0.0108872
$122$	7.06768	0.639878
$123$	−12.2148	−1.10137
$124$	8.12629	0.729763
$125$	−1.00000	−0.0894427
$126$	−1.21400	−0.108152
$127$	−3.87606	−0.343945	−0.171972	−	0.985102i	$-0.555014\pi$
$127$	−3.87606	−0.343945	−0.171972	+	0.985102i	$0.555014\pi$
$128$	1.00000	0.0883883
$129$	−14.8637	−1.30867
$130$	2.77825	0.243669
$131$	19.5526	1.70832	0.854158	−	0.520013i	$-0.174073\pi$
$131$	19.5526	1.70832	0.854158	+	0.520013i	$0.174073\pi$
$132$	6.53408	0.568719
$133$	−10.8538	−0.941142
$134$	−7.92121	−0.684288
$135$	−4.11234	−0.353934
$136$	5.53135	0.474309
$137$	−20.2448	−1.72963	−0.864815	−	0.502090i	$-0.832565\pi$
$137$	−20.2448	−1.72963	−0.864815	+	0.502090i	$0.832565\pi$
$138$	7.80874	0.664724
$139$	−6.87383	−0.583031	−0.291515	−	0.956566i	$-0.594159\pi$
$139$	−6.87383	−0.583031	−0.291515	+	0.956566i	$0.594159\pi$
$140$	1.31383	0.111039
$141$	4.35312	0.366599
$142$	1.57382	0.132072
$143$	9.16412	0.766342
$144$	0.924017	0.0770014
$145$	10.2565	0.851752
$146$	7.48531	0.619488
$147$	10.4470	0.861658
$148$	3.13061	0.257335
$149$	−5.25148	−0.430218	−0.215109	−	0.976590i	$-0.569011\pi$
$149$	−5.25148	−0.430218	−0.215109	+	0.976590i	$0.569011\pi$
$150$	−1.98091	−0.161741
$151$	4.23868	0.344939	0.172470	−	0.985015i	$-0.444825\pi$
$151$	4.23868	0.344939	0.172470	+	0.985015i	$0.444825\pi$
$152$	8.26118	0.670070
$153$	5.11106	0.413205
$154$	4.33369	0.349219
$155$	−8.12629	−0.652720
$156$	5.50347	0.440630
$157$	4.04881	0.323130	0.161565	−	0.986862i	$-0.448346\pi$
$157$	4.04881	0.323130	0.161565	+	0.986862i	$0.448346\pi$
$158$	−8.41541	−0.669494
$159$	−2.81357	−0.223131
$160$	−1.00000	−0.0790569
$161$	5.17910	0.408171
$162$	−10.9182	−0.857818
$163$	18.6247	1.45880	0.729399	−	0.684089i	$-0.239800\pi$
$163$	18.6247	1.45880	0.729399	+	0.684089i	$0.239800\pi$
$164$	6.16623	0.481502
$165$	−6.53408	−0.508678
$166$	−1.48595	−0.115332
$167$	−14.1493	−1.09491	−0.547453	−	0.836836i	$-0.684403\pi$
$167$	−14.1493	−1.09491	−0.547453	+	0.836836i	$0.684403\pi$
$168$	2.60258	0.200794
$169$	−5.28132	−0.406256
$170$	−5.53135	−0.424235
$171$	7.63347	0.583746
$172$	7.50345	0.572133
$173$	−7.52461	−0.572086	−0.286043	−	0.958217i	$-0.592340\pi$
$173$	−7.52461	−0.572086	−0.286043	+	0.958217i	$0.592340\pi$
$174$	20.3172	1.54024
$175$	−1.31383	−0.0993162
$176$	−3.29852	−0.248635
$177$	26.2347	1.97192
$178$	−3.59741	−0.269637
$179$	9.11718	0.681450	0.340725	−	0.940163i	$-0.389327\pi$
$179$	9.11718	0.681450	0.340725	+	0.940163i	$0.389327\pi$
$180$	−0.924017	−0.0688721
$181$	19.2974	1.43436	0.717182	−	0.696886i	$-0.245431\pi$
$181$	19.2974	1.43436	0.717182	+	0.696886i	$0.245431\pi$
$182$	3.65015	0.270567
$183$	−14.0005	−1.03494
$184$	−3.94199	−0.290607
$185$	−3.13061	−0.230167
$186$	−16.0975	−1.18032
$187$	−18.2453	−1.33423
$188$	−2.19753	−0.160271
$189$	−5.40292	−0.393004
$190$	−8.26118	−0.599329
$191$	8.17709	0.591674	0.295837	−	0.955238i	$-0.404402\pi$
$191$	8.17709	0.591674	0.295837	+	0.955238i	$0.404402\pi$
$192$	−1.98091	−0.142960
$193$	−20.9303	−1.50659	−0.753297	−	0.657681i	$-0.771538\pi$
$193$	−20.9303	−1.50659	−0.753297	+	0.657681i	$0.771538\pi$
$194$	−4.31152	−0.309549
$195$	−5.50347	−0.394112
$196$	−5.27385	−0.376704
$197$	4.78440	0.340875	0.170437	−	0.985369i	$-0.445482\pi$
$197$	4.78440	0.340875	0.170437	+	0.985369i	$0.445482\pi$
$198$	−3.04789	−0.216604
$199$	1.00589	0.0713059	0.0356530	−	0.999364i	$-0.488649\pi$
$199$	1.00589	0.0713059	0.0356530	+	0.999364i	$0.488649\pi$
$200$	1.00000	0.0707107
$201$	15.6912	1.10677
$202$	−3.55203	−0.249920
$203$	13.4752	0.945776
$204$	−10.9571	−0.767152
$205$	−6.16623	−0.430668
$206$	−14.9301	−1.04023
$207$	−3.64247	−0.253169
$208$	−2.77825	−0.192637
$209$	−27.2497	−1.88490
$210$	−2.60258	−0.179595
$211$	22.4993	1.54891	0.774457	−	0.632626i	$-0.218023\pi$
$211$	22.4993	1.54891	0.774457	+	0.632626i	$0.218023\pi$
$212$	1.42034	0.0975494
$213$	−3.11759	−0.213614
$214$	−13.8993	−0.950136
$215$	−7.50345	−0.511731
$216$	4.11234	0.279809
$217$	−10.6766	−0.724772
$218$	13.6002	0.921123
$219$	−14.8277	−1.00197
$220$	3.29852	0.222386
$221$	−15.3675	−1.03373
$222$	−6.20147	−0.416216
$223$	−22.0251	−1.47491	−0.737456	−	0.675396i	$-0.763973\pi$
$223$	−22.0251	−1.47491	−0.737456	+	0.675396i	$0.763973\pi$
$224$	−1.31383	−0.0877839
$225$	0.924017	0.0616011
$226$	−12.5287	−0.833397
$227$	−19.5098	−1.29491	−0.647456	−	0.762103i	$-0.724167\pi$
$227$	−19.5098	−1.29491	−0.647456	+	0.762103i	$0.724167\pi$
$228$	−16.3647	−1.08378
$229$	20.8185	1.37573	0.687864	−	0.725840i	$-0.258549\pi$
$229$	20.8185	1.37573	0.687864	+	0.725840i	$0.258549\pi$
$230$	3.94199	0.259927
$231$	−8.58467	−0.564830
$232$	−10.2565	−0.673369
$233$	−14.9189	−0.977372	−0.488686	−	0.872460i	$-0.662524\pi$
$233$	−14.9189	−0.977372	−0.488686	+	0.872460i	$0.662524\pi$
$234$	−2.56715	−0.167820
$235$	2.19753	0.143351
$236$	−13.2437	−0.862093
$237$	16.6702	1.08285
$238$	−7.26725	−0.471066
$239$	−14.8532	−0.960774	−0.480387	−	0.877057i	$-0.659504\pi$
$239$	−14.8532	−0.960774	−0.480387	+	0.877057i	$0.659504\pi$
$240$	1.98091	0.127867
$241$	−21.3767	−1.37699	−0.688497	−	0.725240i	$-0.741729\pi$
$241$	−21.3767	−1.37699	−0.688497	+	0.725240i	$0.741729\pi$
$242$	−0.119759	−0.00769843
$243$	9.29106	0.596022
$244$	7.06768	0.452462
$245$	5.27385	0.336934
$246$	−12.2148	−0.778785
$247$	−22.9516	−1.46038
$248$	8.12629	0.516020
$249$	2.94354	0.186539
$250$	−1.00000	−0.0632456
$251$	11.0413	0.696920	0.348460	−	0.937324i	$-0.386705\pi$
$251$	11.0413	0.696920	0.348460	+	0.937324i	$0.386705\pi$
$252$	−1.21400	−0.0764748
$253$	13.0027	0.817475
$254$	−3.87606	−0.243206
$255$	10.9571	0.686162
$256$	1.00000	0.0625000
$257$	−27.7734	−1.73246	−0.866230	−	0.499646i	$-0.833463\pi$
$257$	−27.7734	−1.73246	−0.866230	+	0.499646i	$0.833463\pi$
$258$	−14.8637	−0.925372
$259$	−4.11309	−0.255575
$260$	2.77825	0.172300
$261$	−9.47714	−0.586620
$262$	19.5526	1.20796
$263$	10.8461	0.668799	0.334400	−	0.942431i	$-0.391467\pi$
$263$	10.8461	0.668799	0.334400	+	0.942431i	$0.391467\pi$
$264$	6.53408	0.402145
$265$	−1.42034	−0.0872508
$266$	−10.8538	−0.665488
$267$	7.12616	0.436114
$268$	−7.92121	−0.483865
$269$	−28.0174	−1.70825	−0.854124	−	0.520069i	$-0.825906\pi$
$269$	−28.0174	−1.70825	−0.854124	+	0.520069i	$0.825906\pi$
$270$	−4.11234	−0.250269
$271$	−3.89139	−0.236385	−0.118192	−	0.992991i	$-0.537710\pi$
$271$	−3.89139	−0.236385	−0.118192	+	0.992991i	$0.537710\pi$
$272$	5.53135	0.335387
$273$	−7.23063	−0.437617
$274$	−20.2448	−1.22303
$275$	−3.29852	−0.198908
$276$	7.80874	0.470031
$277$	−12.9381	−0.777377	−0.388689	−	0.921369i	$-0.627072\pi$
$277$	−12.9381	−0.777377	−0.388689	+	0.921369i	$0.627072\pi$
$278$	−6.87383	−0.412265
$279$	7.50883	0.449542
$280$	1.31383	0.0785163
$281$	7.48817	0.446707	0.223354	−	0.974738i	$-0.428300\pi$
$281$	7.48817	0.446707	0.223354	+	0.974738i	$0.428300\pi$
$282$	4.35312	0.259224
$283$	32.5245	1.93338	0.966691	−	0.255946i	$-0.0823868\pi$
$283$	32.5245	1.93338	0.966691	+	0.255946i	$0.0823868\pi$
$284$	1.57382	0.0933888
$285$	16.3647	0.969360
$286$	9.16412	0.541886
$287$	−8.10137	−0.478209
$288$	0.924017	0.0544482
$289$	13.5958	0.799755
$290$	10.2565	0.602280
$291$	8.54075	0.500668
$292$	7.48531	0.438044
$293$	−8.94250	−0.522427	−0.261213	−	0.965281i	$-0.584123\pi$
$293$	−8.94250	−0.522427	−0.261213	+	0.965281i	$0.584123\pi$
$294$	10.4470	0.609284
$295$	13.2437	0.771080
$296$	3.13061	0.181963
$297$	−13.5646	−0.787101
$298$	−5.25148	−0.304210
$299$	10.9518	0.633361
$300$	−1.98091	−0.114368
$301$	−9.85825	−0.568220
$302$	4.23868	0.243909
$303$	7.03626	0.404222
$304$	8.26118	0.473811
$305$	−7.06768	−0.404694
$306$	5.11106	0.292180
$307$	−9.36171	−0.534301	−0.267151	−	0.963655i	$-0.586082\pi$
$307$	−9.36171	−0.534301	−0.267151	+	0.963655i	$0.586082\pi$
$308$	4.33369	0.246935
$309$	29.5753	1.68248
$310$	−8.12629	−0.461542
$311$	−11.1533	−0.632444	−0.316222	−	0.948685i	$-0.602414\pi$
$311$	−11.1533	−0.632444	−0.316222	+	0.948685i	$0.602414\pi$
$312$	5.50347	0.311573
$313$	−25.1539	−1.42178	−0.710891	−	0.703303i	$-0.751708\pi$
$313$	−25.1539	−1.42178	−0.710891	+	0.703303i	$0.751708\pi$
$314$	4.04881	0.228488
$315$	1.21400	0.0684012
$316$	−8.41541	−0.473404
$317$	25.2786	1.41979	0.709895	−	0.704308i	$-0.248743\pi$
$317$	25.2786	1.41979	0.709895	+	0.704308i	$0.248743\pi$
$318$	−2.81357	−0.157777
$319$	33.8311	1.89418
$320$	−1.00000	−0.0559017
$321$	27.5333	1.53676
$322$	5.17910	0.288620
$323$	45.6955	2.54256
$324$	−10.9182	−0.606569
$325$	−2.77825	−0.154110
$326$	18.6247	1.03153
$327$	−26.9408	−1.48983
$328$	6.16623	0.340473
$329$	2.88718	0.159176
$330$	−6.53408	−0.359689
$331$	14.7240	0.809306	0.404653	−	0.914470i	$-0.367392\pi$
$331$	14.7240	0.809306	0.404653	+	0.914470i	$0.367392\pi$
$332$	−1.48595	−0.0815521
$333$	2.89274	0.158521
$334$	−14.1493	−0.774216
$335$	7.92121	0.432782
$336$	2.60258	0.141982
$337$	−27.1991	−1.48163	−0.740814	−	0.671711i	$-0.765560\pi$
$337$	−27.1991	−1.48163	−0.740814	+	0.671711i	$0.765560\pi$
$338$	−5.28132	−0.287266
$339$	24.8183	1.34794
$340$	−5.53135	−0.299980
$341$	−26.8048	−1.45156
$342$	7.63347	0.412771
$343$	16.1257	0.870709
$344$	7.50345	0.404559
$345$	−7.80874	−0.420408
$346$	−7.52461	−0.404526
$347$	28.4461	1.52707	0.763534	−	0.645767i	$-0.223462\pi$
$347$	28.4461	1.52707	0.763534	+	0.645767i	$0.223462\pi$
$348$	20.3172	1.08911
$349$	−27.0882	−1.45000	−0.724999	−	0.688750i	$-0.758160\pi$
$349$	−27.0882	−1.45000	−0.724999	+	0.688750i	$0.758160\pi$
$350$	−1.31383	−0.0702271
$351$	−11.4251	−0.609828
$352$	−3.29852	−0.175812
$353$	12.1861	0.648602	0.324301	−	0.945954i	$-0.394871\pi$
$353$	12.1861	0.648602	0.324301	+	0.945954i	$0.394871\pi$
$354$	26.2347	1.39436
$355$	−1.57382	−0.0835294
$356$	−3.59741	−0.190662
$357$	14.3958	0.761906
$358$	9.11718	0.481858
$359$	−5.65059	−0.298227	−0.149113	−	0.988820i	$-0.547642\pi$
$359$	−5.65059	−0.298227	−0.149113	+	0.988820i	$0.547642\pi$
$360$	−0.924017	−0.0487000
$361$	49.2471	2.59195
$362$	19.2974	1.01425
$363$	0.237233	0.0124515
$364$	3.65015	0.191320
$365$	−7.48531	−0.391799
$366$	−14.0005	−0.731816
$367$	27.1897	1.41929	0.709645	−	0.704559i	$-0.248855\pi$
$367$	27.1897	1.41929	0.709645	+	0.704559i	$0.248855\pi$
$368$	−3.94199	−0.205490
$369$	5.69770	0.296610
$370$	−3.13061	−0.162753
$371$	−1.86609	−0.0968823
$372$	−16.0975	−0.834616
$373$	−20.2937	−1.05077	−0.525384	−	0.850865i	$-0.676078\pi$
$373$	−20.2937	−1.05077	−0.525384	+	0.850865i	$0.676078\pi$
$374$	−18.2453	−0.943441
$375$	1.98091	0.102294
$376$	−2.19753	−0.113329
$377$	28.4950	1.46757
$378$	−5.40292	−0.277896
$379$	−24.1597	−1.24100	−0.620501	−	0.784206i	$-0.713071\pi$
$379$	−24.1597	−1.24100	−0.620501	+	0.784206i	$0.713071\pi$
$380$	−8.26118	−0.423790
$381$	7.67814	0.393363
$382$	8.17709	0.418376
$383$	32.6040	1.66598	0.832992	−	0.553285i	$-0.186626\pi$
$383$	32.6040	1.66598	0.832992	+	0.553285i	$0.186626\pi$
$384$	−1.98091	−0.101088
$385$	−4.33369	−0.220866
$386$	−20.9303	−1.06532
$387$	6.93331	0.352440
$388$	−4.31152	−0.218884
$389$	−23.9311	−1.21336	−0.606678	−	0.794948i	$-0.707498\pi$
$389$	−23.9311	−1.21336	−0.606678	+	0.794948i	$0.707498\pi$
$390$	−5.50347	−0.278679
$391$	−21.8045	−1.10270
$392$	−5.27385	−0.266370
$393$	−38.7319	−1.95377
$394$	4.78440	0.241035
$395$	8.41541	0.423425
$396$	−3.04789	−0.153162
$397$	−37.3250	−1.87329	−0.936643	−	0.350284i	$-0.886085\pi$
$397$	−37.3250	−1.87329	−0.936643	+	0.350284i	$0.886085\pi$
$398$	1.00589	0.0504209
$399$	21.5004	1.07637
$400$	1.00000	0.0500000
$401$	−8.67881	−0.433399	−0.216699	−	0.976238i	$-0.569529\pi$
$401$	−8.67881	−0.433399	−0.216699	+	0.976238i	$0.569529\pi$
$402$	15.6912	0.782607
$403$	−22.5769	−1.12463
$404$	−3.55203	−0.176720
$405$	10.9182	0.542532
$406$	13.4752	0.668765
$407$	−10.3264	−0.511860
$408$	−10.9571	−0.542459
$409$	25.5701	1.26436	0.632180	−	0.774822i	$-0.282160\pi$
$409$	25.5701	1.26436	0.632180	+	0.774822i	$0.282160\pi$
$410$	−6.16623	−0.304528
$411$	40.1032	1.97815
$412$	−14.9301	−0.735554
$413$	17.4000	0.856198
$414$	−3.64247	−0.179017
$415$	1.48595	0.0729424
$416$	−2.77825	−0.136215
$417$	13.6165	0.666801
$418$	−27.2497	−1.33283
$419$	7.82221	0.382140	0.191070	−	0.981576i	$-0.438804\pi$
$419$	7.82221	0.382140	0.191070	+	0.981576i	$0.438804\pi$
$420$	−2.60258	−0.126993
$421$	−21.3874	−1.04236	−0.521179	−	0.853447i	$-0.674508\pi$
$421$	−21.3874	−1.04236	−0.521179	+	0.853447i	$0.674508\pi$
$422$	22.4993	1.09525
$423$	−2.03056	−0.0987290
$424$	1.42034	0.0689778
$425$	5.53135	0.268310
$426$	−3.11759	−0.151048
$427$	−9.28573	−0.449368
$428$	−13.8993	−0.671848
$429$	−18.1533	−0.876451
$430$	−7.50345	−0.361848
$431$	−3.60041	−0.173426	−0.0867128	−	0.996233i	$-0.527636\pi$
$431$	−3.60041	−0.173426	−0.0867128	+	0.996233i	$0.527636\pi$
$432$	4.11234	0.197855
$433$	−17.1183	−0.822651	−0.411326	−	0.911489i	$-0.634934\pi$
$433$	−17.1183	−0.822651	−0.411326	+	0.911489i	$0.634934\pi$
$434$	−10.6766	−0.512492
$435$	−20.3172	−0.974133
$436$	13.6002	0.651332
$437$	−32.5655	−1.55782
$438$	−14.8277	−0.708497
$439$	−13.0026	−0.620579	−0.310290	−	0.950642i	$-0.600426\pi$
$439$	−13.0026	−0.620579	−0.310290	+	0.950642i	$0.600426\pi$
$440$	3.29852	0.157251
$441$	−4.87313	−0.232054
$442$	−15.3675	−0.730956
$443$	6.59932	0.313543	0.156772	−	0.987635i	$-0.449891\pi$
$443$	6.59932	0.313543	0.156772	+	0.987635i	$0.449891\pi$
$444$	−6.20147	−0.294309
$445$	3.59741	0.170534
$446$	−22.0251	−1.04292
$447$	10.4027	0.492032
$448$	−1.31383	−0.0620726
$449$	−6.71671	−0.316981	−0.158491	−	0.987361i	$-0.550663\pi$
$449$	−6.71671	−0.316981	−0.158491	+	0.987361i	$0.550663\pi$
$450$	0.924017	0.0435586
$451$	−20.3394	−0.957746
$452$	−12.5287	−0.589300
$453$	−8.39646	−0.394500
$454$	−19.5098	−0.915641
$455$	−3.65015	−0.171122
$456$	−16.3647	−0.766346
$457$	29.9134	1.39929	0.699645	−	0.714491i	$-0.253342\pi$
$457$	29.9134	1.39929	0.699645	+	0.714491i	$0.253342\pi$
$458$	20.8185	0.972786
$459$	22.7468	1.06173
$460$	3.94199	0.183796
$461$	−10.2245	−0.476202	−0.238101	−	0.971240i	$-0.576525\pi$
$461$	−10.2245	−0.476202	−0.238101	+	0.971240i	$0.576525\pi$
$462$	−8.58467	−0.399395
$463$	−27.9427	−1.29861	−0.649303	−	0.760529i	$-0.724939\pi$
$463$	−27.9427	−1.29861	−0.649303	+	0.760529i	$0.724939\pi$
$464$	−10.2565	−0.476144
$465$	16.0975	0.746503
$466$	−14.9189	−0.691106
$467$	2.30119	0.106486	0.0532432	−	0.998582i	$-0.483044\pi$
$467$	2.30119	0.106486	0.0532432	+	0.998582i	$0.483044\pi$
$468$	−2.56715	−0.118667
$469$	10.4071	0.480556
$470$	2.19753	0.101365
$471$	−8.02034	−0.369558
$472$	−13.2437	−0.609592
$473$	−24.7503	−1.13802
$474$	16.6702	0.765688
$475$	8.26118	0.379049
$476$	−7.26725	−0.333094
$477$	1.31242	0.0600915
$478$	−14.8532	−0.679370
$479$	13.0078	0.594341	0.297171	−	0.954824i	$-0.403957\pi$
$479$	13.0078	0.594341	0.297171	+	0.954824i	$0.403957\pi$
$480$	1.98091	0.0904159
$481$	−8.69763	−0.396578
$482$	−21.3767	−0.973681
$483$	−10.2594	−0.466817
$484$	−0.119759	−0.00544361
$485$	4.31152	0.195776
$486$	9.29106	0.421451
$487$	−0.873252	−0.0395708	−0.0197854	−	0.999804i	$-0.506298\pi$
$487$	−0.873252	−0.0395708	−0.0197854	+	0.999804i	$0.506298\pi$
$488$	7.06768	0.319939
$489$	−36.8939	−1.66840
$490$	5.27385	0.238248
$491$	11.5044	0.519189	0.259594	−	0.965718i	$-0.416411\pi$
$491$	11.5044	0.519189	0.259594	+	0.965718i	$0.416411\pi$
$492$	−12.2148	−0.550684
$493$	−56.7321	−2.55508
$494$	−22.9516	−1.03264
$495$	3.04789	0.136992
$496$	8.12629	0.364881
$497$	−2.06773	−0.0927501
$498$	2.94354	0.131903
$499$	−3.02658	−0.135488	−0.0677441	−	0.997703i	$-0.521580\pi$
$499$	−3.02658	−0.135488	−0.0677441	+	0.997703i	$0.521580\pi$
$500$	−1.00000	−0.0447214
$501$	28.0286	1.25222
$502$	11.0413	0.492797
$503$	−5.40204	−0.240865	−0.120432	−	0.992722i	$-0.538428\pi$
$503$	−5.40204	−0.240865	−0.120432	+	0.992722i	$0.538428\pi$
$504$	−1.21400	−0.0540759
$505$	3.55203	0.158063
$506$	13.0027	0.578042
$507$	10.4618	0.464627
$508$	−3.87606	−0.171972
$509$	−21.1827	−0.938905	−0.469453	−	0.882958i	$-0.655549\pi$
$509$	−21.1827	−0.938905	−0.469453	+	0.882958i	$0.655549\pi$
$510$	10.9571	0.485190
$511$	−9.83442	−0.435049
$512$	1.00000	0.0441942
$513$	33.9728	1.49994
$514$	−27.7734	−1.22503
$515$	14.9301	0.657900
$516$	−14.8637	−0.654337
$517$	7.24860	0.318793
$518$	−4.11309	−0.180719
$519$	14.9056	0.654283
$520$	2.77825	0.121834
$521$	18.7295	0.820555	0.410278	−	0.911961i	$-0.365432\pi$
$521$	18.7295	0.820555	0.410278	+	0.911961i	$0.365432\pi$
$522$	−9.47714	−0.414803
$523$	−31.1721	−1.36306	−0.681530	−	0.731790i	$-0.738685\pi$
$523$	−31.1721	−1.36306	−0.681530	+	0.731790i	$0.738685\pi$
$524$	19.5526	0.854158
$525$	2.60258	0.113586
$526$	10.8461	0.472912
$527$	44.9494	1.95803
$528$	6.53408	0.284359
$529$	−7.46071	−0.324379
$530$	−1.42034	−0.0616957
$531$	−12.2374	−0.531059
$532$	−10.8538	−0.470571
$533$	−17.1313	−0.742040
$534$	7.12616	0.308379
$535$	13.8993	0.600919
$536$	−7.92121	−0.342144
$537$	−18.0603	−0.779361
$538$	−28.0174	−1.20791
$539$	17.3959	0.749295
$540$	−4.11234	−0.176967
$541$	5.31899	0.228681	0.114341	−	0.993442i	$-0.463524\pi$
$541$	5.31899	0.228681	0.114341	+	0.993442i	$0.463524\pi$
$542$	−3.89139	−0.167149
$543$	−38.2265	−1.64046
$544$	5.53135	0.237155
$545$	−13.6002	−0.582569
$546$	−7.23063	−0.309442
$547$	5.07270	0.216893	0.108446	−	0.994102i	$-0.465412\pi$
$547$	5.07270	0.216893	0.108446	+	0.994102i	$0.465412\pi$
$548$	−20.2448	−0.864815
$549$	6.53066	0.278722
$550$	−3.29852	−0.140649
$551$	−84.7304	−3.60964
$552$	7.80874	0.332362
$553$	11.0564	0.470167
$554$	−12.9381	−0.549689
$555$	6.20147	0.263238
$556$	−6.87383	−0.291515
$557$	2.33242	0.0988279	0.0494140	−	0.998778i	$-0.484265\pi$
$557$	2.33242	0.0988279	0.0494140	+	0.998778i	$0.484265\pi$
$558$	7.50883	0.317874
$559$	−20.8465	−0.881711
$560$	1.31383	0.0555194
$561$	36.1423	1.52593
$562$	7.48817	0.315870
$563$	29.9165	1.26083	0.630415	−	0.776258i	$-0.282885\pi$
$563$	29.9165	1.26083	0.630415	+	0.776258i	$0.282885\pi$
$564$	4.35312	0.183299
$565$	12.5287	0.527086
$566$	32.5245	1.36711
$567$	14.3447	0.602421
$568$	1.57382	0.0660358
$569$	−19.9291	−0.835473	−0.417737	−	0.908568i	$-0.637176\pi$
$569$	−19.9291	−0.835473	−0.417737	+	0.908568i	$0.637176\pi$
$570$	16.3647	0.685441
$571$	−21.8627	−0.914926	−0.457463	−	0.889229i	$-0.651242\pi$
$571$	−21.8627	−0.914926	−0.457463	+	0.889229i	$0.651242\pi$
$572$	9.16412	0.383171
$573$	−16.1981	−0.676686
$574$	−8.10137	−0.338145
$575$	−3.94199	−0.164392
$576$	0.924017	0.0385007
$577$	−0.122394	−0.00509532	−0.00254766	−	0.999997i	$-0.500811\pi$
$577$	−0.122394	−0.00509532	−0.00254766	+	0.999997i	$0.500811\pi$
$578$	13.5958	0.565512
$579$	41.4610	1.72306
$580$	10.2565	0.425876
$581$	1.95228	0.0809944
$582$	8.54075	0.354026
$583$	−4.68502	−0.194034
$584$	7.48531	0.309744
$585$	2.56715	0.106139
$586$	−8.94250	−0.369411
$587$	−20.3492	−0.839901	−0.419951	−	0.907547i	$-0.637953\pi$
$587$	−20.3492	−0.839901	−0.419951	+	0.907547i	$0.637953\pi$
$588$	10.4470	0.430829
$589$	67.1328	2.76616
$590$	13.2437	0.545236
$591$	−9.47749	−0.389852
$592$	3.13061	0.128667
$593$	−18.3054	−0.751712	−0.375856	−	0.926678i	$-0.622651\pi$
$593$	−18.3054	−0.751712	−0.375856	+	0.926678i	$0.622651\pi$
$594$	−13.5646	−0.556564
$595$	7.26725	0.297928
$596$	−5.25148	−0.215109
$597$	−1.99259	−0.0815512
$598$	10.9518	0.447854
$599$	24.6536	1.00732	0.503659	−	0.863902i	$-0.331987\pi$
$599$	24.6536	1.00732	0.503659	+	0.863902i	$0.331987\pi$
$600$	−1.98091	−0.0808704
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−9.85825	−0.401792
$603$	−7.31933	−0.298066
$604$	4.23868	0.172470
$605$	0.119759	0.00486891
$606$	7.03626	0.285828
$607$	30.1504	1.22377	0.611884	−	0.790948i	$-0.290412\pi$
$607$	30.1504	1.22377	0.611884	+	0.790948i	$0.290412\pi$
$608$	8.26118	0.335035
$609$	−26.6933	−1.08167
$610$	−7.06768	−0.286162
$611$	6.10529	0.246994
$612$	5.11106	0.206602
$613$	−20.6446	−0.833826	−0.416913	−	0.908946i	$-0.636888\pi$
$613$	−20.6446	−0.833826	−0.416913	+	0.908946i	$0.636888\pi$
$614$	−9.36171	−0.377808
$615$	12.2148	0.492547
$616$	4.33369	0.174610
$617$	29.7476	1.19759	0.598797	−	0.800901i	$-0.295646\pi$
$617$	29.7476	1.19759	0.598797	+	0.800901i	$0.295646\pi$
$618$	29.5753	1.18969
$619$	−20.2098	−0.812300	−0.406150	−	0.913806i	$-0.633129\pi$
$619$	−20.2098	−0.812300	−0.406150	+	0.913806i	$0.633129\pi$
$620$	−8.12629	−0.326360
$621$	−16.2108	−0.650518
$622$	−11.1533	−0.447205
$623$	4.72638	0.189359
$624$	5.50347	0.220315
$625$	1.00000	0.0400000
$626$	−25.1539	−1.00535
$627$	53.9792	2.15572
$628$	4.04881	0.161565
$629$	17.3165	0.690455
$630$	1.21400	0.0483669
$631$	2.15178	0.0856609	0.0428305	−	0.999082i	$-0.486362\pi$
$631$	2.15178	0.0856609	0.0428305	+	0.999082i	$0.486362\pi$
$632$	−8.41541	−0.334747
$633$	−44.5691	−1.77146
$634$	25.2786	1.00394
$635$	3.87606	0.153817
$636$	−2.81357	−0.111565
$637$	14.6521	0.580537
$638$	33.8311	1.33939
$639$	1.45423	0.0575285
$640$	−1.00000	−0.0395285
$641$	−30.7828	−1.21585	−0.607924	−	0.793995i	$-0.707997\pi$
$641$	−30.7828	−1.21585	−0.607924	+	0.793995i	$0.707997\pi$
$642$	27.5333	1.08665
$643$	−9.47083	−0.373493	−0.186747	−	0.982408i	$-0.559794\pi$
$643$	−9.47083	−0.373493	−0.186747	+	0.982408i	$0.559794\pi$
$644$	5.17910	0.204085
$645$	14.8637	0.585257
$646$	45.6955	1.79786
$647$	−23.0676	−0.906879	−0.453440	−	0.891287i	$-0.649803\pi$
$647$	−23.0676	−0.906879	−0.453440	+	0.891287i	$0.649803\pi$
$648$	−10.9182	−0.428909
$649$	43.6847	1.71477
$650$	−2.77825	−0.108972
$651$	21.1493	0.828908
$652$	18.6247	0.729399
$653$	−44.1665	−1.72837	−0.864183	−	0.503177i	$-0.832164\pi$
$653$	−44.1665	−1.72837	−0.864183	+	0.503177i	$0.832164\pi$
$654$	−26.9408	−1.05347
$655$	−19.5526	−0.763982
$656$	6.16623	0.240751
$657$	6.91655	0.269840
$658$	2.88718	0.112554
$659$	18.3623	0.715294	0.357647	−	0.933857i	$-0.383579\pi$
$659$	18.3623	0.715294	0.357647	+	0.933857i	$0.383579\pi$
$660$	−6.53408	−0.254339
$661$	−35.5783	−1.38384	−0.691919	−	0.721976i	$-0.743234\pi$
$661$	−35.5783	−1.38384	−0.691919	+	0.721976i	$0.743234\pi$
$662$	14.7240	0.572266
$663$	30.4416	1.18226
$664$	−1.48595	−0.0576660
$665$	10.8538	0.420892
$666$	2.89274	0.112091
$667$	40.4309	1.56549
$668$	−14.1493	−0.547453
$669$	43.6299	1.68683
$670$	7.92121	0.306023
$671$	−23.3129	−0.899984
$672$	2.60258	0.100397
$673$	−21.1022	−0.813431	−0.406716	−	0.913555i	$-0.633326\pi$
$673$	−21.1022	−0.813431	−0.406716	+	0.913555i	$0.633326\pi$
$674$	−27.1991	−1.04767
$675$	4.11234	0.158284
$676$	−5.28132	−0.203128
$677$	−17.2167	−0.661693	−0.330847	−	0.943685i	$-0.607334\pi$
$677$	−17.2167	−0.661693	−0.330847	+	0.943685i	$0.607334\pi$
$678$	24.8183	0.953140
$679$	5.66461	0.217388
$680$	−5.53135	−0.212118
$681$	38.6473	1.48097
$682$	−26.8048	−1.02641
$683$	4.31658	0.165169	0.0825847	−	0.996584i	$-0.473683\pi$
$683$	4.31658	0.165169	0.0825847	+	0.996584i	$0.473683\pi$
$684$	7.63347	0.291873
$685$	20.2448	0.773514
$686$	16.1257	0.615684
$687$	−41.2397	−1.57339
$688$	7.50345	0.286066
$689$	−3.94606	−0.150333
$690$	−7.80874	−0.297274
$691$	−7.12201	−0.270934	−0.135467	−	0.990782i	$-0.543253\pi$
$691$	−7.12201	−0.270934	−0.135467	+	0.990782i	$0.543253\pi$
$692$	−7.52461	−0.286043
$693$	4.00441	0.152115
$694$	28.4461	1.07980
$695$	6.87383	0.260739
$696$	20.3172	0.770120
$697$	34.1076	1.29192
$698$	−27.0882	−1.02530
$699$	29.5531	1.11780
$700$	−1.31383	−0.0496581
$701$	25.0454	0.945950	0.472975	−	0.881076i	$-0.343180\pi$
$701$	25.0454	0.945950	0.472975	+	0.881076i	$0.343180\pi$
$702$	−11.4251	−0.431213
$703$	25.8626	0.975425
$704$	−3.29852	−0.124318
$705$	−4.35312	−0.163948
$706$	12.1861	0.458631
$707$	4.66676	0.175511
$708$	26.2347	0.985959
$709$	−12.0351	−0.451988	−0.225994	−	0.974129i	$-0.572563\pi$
$709$	−12.0351	−0.451988	−0.225994	+	0.974129i	$0.572563\pi$
$710$	−1.57382	−0.0590642
$711$	−7.77598	−0.291622
$712$	−3.59741	−0.134819
$713$	−32.0338	−1.19967
$714$	14.3958	0.538749
$715$	−9.16412	−0.342719
$716$	9.11718	0.340725
$717$	29.4229	1.09882
$718$	−5.65059	−0.210878
$719$	−13.0905	−0.488194	−0.244097	−	0.969751i	$-0.578492\pi$
$719$	−13.0905	−0.488194	−0.244097	+	0.969751i	$0.578492\pi$
$720$	−0.924017	−0.0344361
$721$	19.6156	0.730524
$722$	49.2471	1.83279
$723$	42.3453	1.57484
$724$	19.2974	0.717182
$725$	−10.2565	−0.380915
$726$	0.237233	0.00880454
$727$	−37.8362	−1.40327	−0.701633	−	0.712538i	$-0.747545\pi$
$727$	−37.8362	−1.40327	−0.701633	+	0.712538i	$0.747545\pi$
$728$	3.65015	0.135283
$729$	14.3499	0.531479
$730$	−7.48531	−0.277044
$731$	41.5042	1.53509
$732$	−14.0005	−0.517472
$733$	−37.5141	−1.38561	−0.692807	−	0.721123i	$-0.743626\pi$
$733$	−37.5141	−1.38561	−0.692807	+	0.721123i	$0.743626\pi$
$734$	27.1897	1.00359
$735$	−10.4470	−0.385345
$736$	−3.94199	−0.145304
$737$	26.1283	0.962447
$738$	5.69770	0.209735
$739$	23.2386	0.854847	0.427424	−	0.904051i	$-0.359421\pi$
$739$	23.2386	0.854847	0.427424	+	0.904051i	$0.359421\pi$
$740$	−3.13061	−0.115084
$741$	45.4652	1.67021
$742$	−1.86609	−0.0685062
$743$	−23.1797	−0.850381	−0.425191	−	0.905104i	$-0.639793\pi$
$743$	−23.1797	−0.850381	−0.425191	+	0.905104i	$0.639793\pi$
$744$	−16.0975	−0.590162
$745$	5.25148	0.192399
$746$	−20.2937	−0.743005
$747$	−1.37304	−0.0502370
$748$	−18.2453	−0.667113
$749$	18.2613	0.667254
$750$	1.98091	0.0723327
$751$	−35.3347	−1.28938	−0.644692	−	0.764443i	$-0.723014\pi$
$751$	−35.3347	−1.28938	−0.644692	+	0.764443i	$0.723014\pi$
$752$	−2.19753	−0.0801357
$753$	−21.8718	−0.797054
$754$	28.4950	1.03773
$755$	−4.23868	−0.154261
$756$	−5.40292	−0.196502
$757$	−24.1948	−0.879376	−0.439688	−	0.898151i	$-0.644911\pi$
$757$	−24.1948	−0.879376	−0.439688	+	0.898151i	$0.644911\pi$
$758$	−24.1597	−0.877521
$759$	−25.7573	−0.934931
$760$	−8.26118	−0.299665
$761$	37.3782	1.35496	0.677480	−	0.735541i	$-0.263072\pi$
$761$	37.3782	1.35496	0.677480	+	0.735541i	$0.263072\pi$
$762$	7.67814	0.278150
$763$	−17.8684	−0.646878
$764$	8.17709	0.295837
$765$	−5.11106	−0.184791
$766$	32.6040	1.17803
$767$	36.7944	1.32857
$768$	−1.98091	−0.0714800
$769$	50.7004	1.82830	0.914151	−	0.405373i	$-0.132858\pi$
$769$	50.7004	1.82830	0.914151	+	0.405373i	$0.132858\pi$
$770$	−4.33369	−0.156175
$771$	55.0168	1.98138
$772$	−20.9303	−0.753297
$773$	15.8476	0.570000	0.285000	−	0.958527i	$-0.408006\pi$
$773$	15.8476	0.570000	0.285000	+	0.958527i	$0.408006\pi$
$774$	6.93331	0.249213
$775$	8.12629	0.291905
$776$	−4.31152	−0.154775
$777$	8.14768	0.292296
$778$	−23.9311	−0.857972
$779$	50.9403	1.82513
$780$	−5.50347	−0.197056
$781$	−5.19126	−0.185758
$782$	−21.8045	−0.779728
$783$	−42.1781	−1.50732
$784$	−5.27385	−0.188352
$785$	−4.04881	−0.144508
$786$	−38.7319	−1.38152
$787$	−34.3178	−1.22330	−0.611648	−	0.791130i	$-0.709493\pi$
$787$	−34.3178	−1.22330	−0.611648	+	0.791130i	$0.709493\pi$
$788$	4.78440	0.170437
$789$	−21.4852	−0.764893
$790$	8.41541	0.299407
$791$	16.4606	0.585271
$792$	−3.04789	−0.108302
$793$	−19.6358	−0.697287
$794$	−37.3250	−1.32461
$795$	2.81357	0.0997871
$796$	1.00589	0.0356530
$797$	−14.7784	−0.523476	−0.261738	−	0.965139i	$-0.584296\pi$
$797$	−14.7784	−0.523476	−0.261738	+	0.965139i	$0.584296\pi$
$798$	21.5004	0.761106
$799$	−12.1553	−0.430024
$800$	1.00000	0.0353553
$801$	−3.32407	−0.117450
$802$	−8.67881	−0.306459
$803$	−24.6904	−0.871307
$804$	15.6912	0.553387
$805$	−5.17910	−0.182539
$806$	−22.5769	−0.795237
$807$	55.5000	1.95369
$808$	−3.55203	−0.124960
$809$	45.3373	1.59397	0.796987	−	0.603996i	$-0.206426\pi$
$809$	45.3373	1.59397	0.796987	+	0.603996i	$0.206426\pi$
$810$	10.9182	0.383628
$811$	30.6792	1.07729	0.538646	−	0.842532i	$-0.318936\pi$
$811$	30.6792	1.07729	0.538646	+	0.842532i	$0.318936\pi$
$812$	13.4752	0.472888
$813$	7.70850	0.270349
$814$	−10.3264	−0.361940
$815$	−18.6247	−0.652394
$816$	−10.9571	−0.383576
$817$	61.9873	2.16866
$818$	25.5701	0.894037
$819$	3.37280	0.117855
$820$	−6.16623	−0.215334
$821$	5.38341	0.187882	0.0939412	−	0.995578i	$-0.470053\pi$
$821$	5.38341	0.187882	0.0939412	+	0.995578i	$0.470053\pi$
$822$	40.1032	1.39876
$823$	12.3172	0.429350	0.214675	−	0.976686i	$-0.431131\pi$
$823$	12.3172	0.429350	0.214675	+	0.976686i	$0.431131\pi$
$824$	−14.9301	−0.520115
$825$	6.53408	0.227488
$826$	17.4000	0.605423
$827$	46.3008	1.61004	0.805019	−	0.593249i	$-0.202155\pi$
$827$	46.3008	1.61004	0.805019	+	0.593249i	$0.202155\pi$
$828$	−3.64247	−0.126584
$829$	−5.00492	−0.173828	−0.0869141	−	0.996216i	$-0.527701\pi$
$829$	−5.00492	−0.173828	−0.0869141	+	0.996216i	$0.527701\pi$
$830$	1.48595	0.0515781
$831$	25.6293	0.889072
$832$	−2.77825	−0.0963185
$833$	−29.1715	−1.01073
$834$	13.6165	0.471499
$835$	14.1493	0.489657
$836$	−27.2497	−0.942450
$837$	33.4181	1.15510
$838$	7.82221	0.270214
$839$	−23.0497	−0.795764	−0.397882	−	0.917437i	$-0.630255\pi$
$839$	−23.0497	−0.795764	−0.397882	+	0.917437i	$0.630255\pi$
$840$	−2.60258	−0.0897976
$841$	76.1949	2.62741
$842$	−21.3874	−0.737058
$843$	−14.8334	−0.510890
$844$	22.4993	0.774457
$845$	5.28132	0.181683
$846$	−2.03056	−0.0698120
$847$	0.157343	0.00540639
$848$	1.42034	0.0487747
$849$	−64.4283	−2.21117
$850$	5.53135	0.189724
$851$	−12.3409	−0.423039
$852$	−3.11759	−0.106807
$853$	26.0330	0.891351	0.445676	−	0.895194i	$-0.352963\pi$
$853$	26.0330	0.891351	0.445676	+	0.895194i	$0.352963\pi$
$854$	−9.28573	−0.317751
$855$	−7.63347	−0.261059
$856$	−13.8993	−0.475068
$857$	−18.2641	−0.623890	−0.311945	−	0.950100i	$-0.600980\pi$
$857$	−18.2641	−0.623890	−0.311945	+	0.950100i	$0.600980\pi$
$858$	−18.1533	−0.619744
$859$	20.5232	0.700242	0.350121	−	0.936705i	$-0.386141\pi$
$859$	20.5232	0.700242	0.350121	+	0.936705i	$0.386141\pi$
$860$	−7.50345	−0.255865
$861$	16.0481	0.546918
$862$	−3.60041	−0.122630
$863$	−2.77450	−0.0944450	−0.0472225	−	0.998884i	$-0.515037\pi$
$863$	−2.77450	−0.0944450	−0.0472225	+	0.998884i	$0.515037\pi$
$864$	4.11234	0.139905
$865$	7.52461	0.255845
$866$	−17.1183	−0.581702
$867$	−26.9322	−0.914665
$868$	−10.6766	−0.362386
$869$	27.7584	0.941640
$870$	−20.3172	−0.688816
$871$	22.0071	0.745682
$872$	13.6002	0.460561
$873$	−3.98392	−0.134835
$874$	−32.5655	−1.10154
$875$	1.31383	0.0444155
$876$	−14.8277	−0.500983
$877$	7.39004	0.249544	0.124772	−	0.992185i	$-0.460180\pi$
$877$	7.39004	0.249544	0.124772	+	0.992185i	$0.460180\pi$
$878$	−13.0026	−0.438816
$879$	17.7143	0.597489
$880$	3.29852	0.111193
$881$	9.92938	0.334529	0.167265	−	0.985912i	$-0.446507\pi$
$881$	9.92938	0.334529	0.167265	+	0.985912i	$0.446507\pi$
$882$	−4.87313	−0.164087
$883$	45.0463	1.51593	0.757964	−	0.652296i	$-0.226194\pi$
$883$	45.0463	1.51593	0.757964	+	0.652296i	$0.226194\pi$
$884$	−15.3675	−0.516864
$885$	−26.2347	−0.881869
$886$	6.59932	0.221709
$887$	31.8856	1.07061	0.535307	−	0.844658i	$-0.320196\pi$
$887$	31.8856	1.07061	0.535307	+	0.844658i	$0.320196\pi$
$888$	−6.20147	−0.208108
$889$	5.09248	0.170796
$890$	3.59741	0.120585
$891$	36.0141	1.20652
$892$	−22.0251	−0.737456
$893$	−18.1542	−0.607507
$894$	10.4027	0.347919
$895$	−9.11718	−0.304754
$896$	−1.31383	−0.0438920
$897$	−21.6946	−0.724363
$898$	−6.71671	−0.224139
$899$	−83.3470	−2.77978
$900$	0.924017	0.0308006
$901$	7.85640	0.261735
$902$	−20.3394	−0.677229
$903$	19.5283	0.649862
$904$	−12.5287	−0.416698
$905$	−19.2974	−0.641467
$906$	−8.39646	−0.278954
$907$	−24.9312	−0.827826	−0.413913	−	0.910316i	$-0.635838\pi$
$907$	−24.9312	−0.827826	−0.413913	+	0.910316i	$0.635838\pi$
$908$	−19.5098	−0.647456
$909$	−3.28213	−0.108861
$910$	−3.65015	−0.121001
$911$	30.2873	1.00346	0.501732	−	0.865023i	$-0.332696\pi$
$911$	30.2873	1.00346	0.501732	+	0.865023i	$0.332696\pi$
$912$	−16.3647	−0.541889
$913$	4.90143	0.162214
$914$	29.9134	0.989447
$915$	14.0005	0.462841
$916$	20.8185	0.687864
$917$	−25.6887	−0.848317
$918$	22.7468	0.750757
$919$	6.23159	0.205561	0.102781	−	0.994704i	$-0.467226\pi$
$919$	6.23159	0.205561	0.102781	+	0.994704i	$0.467226\pi$
$920$	3.94199	0.129964
$921$	18.5447	0.611070
$922$	−10.2245	−0.336726
$923$	−4.37245	−0.143921
$924$	−8.58467	−0.282415
$925$	3.13061	0.102934
$926$	−27.9427	−0.918254
$927$	−13.7957	−0.453110
$928$	−10.2565	−0.336685
$929$	4.39215	0.144102	0.0720509	−	0.997401i	$-0.477046\pi$
$929$	4.39215	0.144102	0.0720509	+	0.997401i	$0.477046\pi$
$930$	16.0975	0.527857
$931$	−43.5682	−1.42789
$932$	−14.9189	−0.488686
$933$	22.0936	0.723314
$934$	2.30119	0.0752973
$935$	18.2453	0.596684
$936$	−2.56715	−0.0839099
$937$	34.1948	1.11710	0.558548	−	0.829472i	$-0.311359\pi$
$937$	34.1948	1.11710	0.558548	+	0.829472i	$0.311359\pi$
$938$	10.4071	0.339804
$939$	49.8276	1.62606
$940$	2.19753	0.0716756
$941$	28.1014	0.916080	0.458040	−	0.888932i	$-0.348552\pi$
$941$	28.1014	0.916080	0.458040	+	0.888932i	$0.348552\pi$
$942$	−8.02034	−0.261317
$943$	−24.3072	−0.791552
$944$	−13.2437	−0.431047
$945$	5.40292	0.175757
$946$	−24.7503	−0.804701
$947$	−37.4174	−1.21590	−0.607952	−	0.793974i	$-0.708009\pi$
$947$	−37.4174	−1.21590	−0.607952	+	0.793974i	$0.708009\pi$
$948$	16.6702	0.541423
$949$	−20.7961	−0.675069
$950$	8.26118	0.268028
$951$	−50.0748	−1.62379
$952$	−7.26725	−0.235533
$953$	−30.1560	−0.976849	−0.488424	−	0.872606i	$-0.662428\pi$
$953$	−30.1560	−0.976849	−0.488424	+	0.872606i	$0.662428\pi$
$954$	1.31242	0.0424911
$955$	−8.17709	−0.264605
$956$	−14.8532	−0.480387
$957$	−67.0166	−2.16634
$958$	13.0078	0.420263
$959$	26.5982	0.858902
$960$	1.98091	0.0639337
$961$	35.0367	1.13021
$962$	−8.69763	−0.280423
$963$	−12.8432	−0.413866
$964$	−21.3767	−0.688497
$965$	20.9303	0.673769
$966$	−10.2594	−0.330089
$967$	43.8620	1.41051	0.705253	−	0.708956i	$-0.250833\pi$
$967$	43.8620	1.41051	0.705253	+	0.708956i	$0.250833\pi$
$968$	−0.119759	−0.00384921
$969$	−90.5188	−2.90788
$970$	4.31152	0.138435
$971$	−6.78338	−0.217689	−0.108844	−	0.994059i	$-0.534715\pi$
$971$	−6.78338	−0.217689	−0.108844	+	0.994059i	$0.534715\pi$
$972$	9.29106	0.298011
$973$	9.03104	0.289522
$974$	−0.873252	−0.0279808
$975$	5.50347	0.176252
$976$	7.06768	0.226231
$977$	−12.5360	−0.401061	−0.200531	−	0.979687i	$-0.564267\pi$
$977$	−12.5360	−0.401061	−0.200531	+	0.979687i	$0.564267\pi$
$978$	−36.8939	−1.17974
$979$	11.8661	0.379243
$980$	5.27385	0.168467
$981$	12.5668	0.401228
$982$	11.5044	0.367122
$983$	29.6293	0.945029	0.472515	−	0.881323i	$-0.343346\pi$
$983$	29.6293	0.945029	0.472515	+	0.881323i	$0.343346\pi$
$984$	−12.2148	−0.389392
$985$	−4.78440	−0.152444
$986$	−56.7321	−1.80672
$987$	−5.71926	−0.182046
$988$	−22.9516	−0.730189
$989$	−29.5785	−0.940542
$990$	3.04789	0.0968683
$991$	−50.8716	−1.61599	−0.807995	−	0.589189i	$-0.799447\pi$
$991$	−50.8716	−1.61599	−0.807995	+	0.589189i	$0.799447\pi$
$992$	8.12629	0.258010
$993$	−29.1670	−0.925588
$994$	−2.06773	−0.0655843
$995$	−1.00589	−0.0318890
$996$	2.94354	0.0932695
$997$	19.0359	0.602872	0.301436	−	0.953486i	$-0.402534\pi$
$997$	19.0359	0.602872	0.301436	+	0.953486i	$0.402534\pi$
$998$	−3.02658	−0.0958046
$999$	12.8742	0.407320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.5	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.98091 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98091 q^{6} -1.31383 q^{7} +1.00000 q^{8} +0.924017 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.98091 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98091 q^{6} -1.31383 q^{7} +1.00000 q^{8} +0.924017 q^{9} -1.00000 q^{10} -3.29852 q^{11} -1.98091 q^{12} -2.77825 q^{13} -1.31383 q^{14} +1.98091 q^{15} +1.00000 q^{16} +5.53135 q^{17} +0.924017 q^{18} +8.26118 q^{19} -1.00000 q^{20} +2.60258 q^{21} -3.29852 q^{22} -3.94199 q^{23} -1.98091 q^{24} +1.00000 q^{25} -2.77825 q^{26} +4.11234 q^{27} -1.31383 q^{28} -10.2565 q^{29} +1.98091 q^{30} +8.12629 q^{31} +1.00000 q^{32} +6.53408 q^{33} +5.53135 q^{34} +1.31383 q^{35} +0.924017 q^{36} +3.13061 q^{37} +8.26118 q^{38} +5.50347 q^{39} -1.00000 q^{40} +6.16623 q^{41} +2.60258 q^{42} +7.50345 q^{43} -3.29852 q^{44} -0.924017 q^{45} -3.94199 q^{46} -2.19753 q^{47} -1.98091 q^{48} -5.27385 q^{49} +1.00000 q^{50} -10.9571 q^{51} -2.77825 q^{52} +1.42034 q^{53} +4.11234 q^{54} +3.29852 q^{55} -1.31383 q^{56} -16.3647 q^{57} -10.2565 q^{58} -13.2437 q^{59} +1.98091 q^{60} +7.06768 q^{61} +8.12629 q^{62} -1.21400 q^{63} +1.00000 q^{64} +2.77825 q^{65} +6.53408 q^{66} -7.92121 q^{67} +5.53135 q^{68} +7.80874 q^{69} +1.31383 q^{70} +1.57382 q^{71} +0.924017 q^{72} +7.48531 q^{73} +3.13061 q^{74} -1.98091 q^{75} +8.26118 q^{76} +4.33369 q^{77} +5.50347 q^{78} -8.41541 q^{79} -1.00000 q^{80} -10.9182 q^{81} +6.16623 q^{82} -1.48595 q^{83} +2.60258 q^{84} -5.53135 q^{85} +7.50345 q^{86} +20.3172 q^{87} -3.29852 q^{88} -3.59741 q^{89} -0.924017 q^{90} +3.65015 q^{91} -3.94199 q^{92} -16.0975 q^{93} -2.19753 q^{94} -8.26118 q^{95} -1.98091 q^{96} -4.31152 q^{97} -5.27385 q^{98} -3.04789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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