LMFDB - Embedded newform 6034.2.a.n.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.43998 q^{3} +1.00000 q^{4} +0.943876 q^{5} -2.43998 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.95349 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.43998 q^{3} +1.00000 q^{4} +0.943876 q^{5} -2.43998 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.95349 q^{9} -0.943876 q^{10} +0.679577 q^{11} +2.43998 q^{12} +6.21936 q^{13} +1.00000 q^{14} +2.30304 q^{15} +1.00000 q^{16} +5.66666 q^{17} -2.95349 q^{18} +5.13641 q^{19} +0.943876 q^{20} -2.43998 q^{21} -0.679577 q^{22} -1.80201 q^{23} -2.43998 q^{24} -4.10910 q^{25} -6.21936 q^{26} -0.113478 q^{27} -1.00000 q^{28} +2.77702 q^{29} -2.30304 q^{30} +2.08433 q^{31} -1.00000 q^{32} +1.65815 q^{33} -5.66666 q^{34} -0.943876 q^{35} +2.95349 q^{36} -5.86143 q^{37} -5.13641 q^{38} +15.1751 q^{39} -0.943876 q^{40} +3.44758 q^{41} +2.43998 q^{42} -3.18527 q^{43} +0.679577 q^{44} +2.78773 q^{45} +1.80201 q^{46} +6.61137 q^{47} +2.43998 q^{48} +1.00000 q^{49} +4.10910 q^{50} +13.8265 q^{51} +6.21936 q^{52} -1.94856 q^{53} +0.113478 q^{54} +0.641437 q^{55} +1.00000 q^{56} +12.5327 q^{57} -2.77702 q^{58} -6.17997 q^{59} +2.30304 q^{60} +10.3670 q^{61} -2.08433 q^{62} -2.95349 q^{63} +1.00000 q^{64} +5.87031 q^{65} -1.65815 q^{66} +2.57691 q^{67} +5.66666 q^{68} -4.39688 q^{69} +0.943876 q^{70} -2.07951 q^{71} -2.95349 q^{72} +0.542587 q^{73} +5.86143 q^{74} -10.0261 q^{75} +5.13641 q^{76} -0.679577 q^{77} -15.1751 q^{78} -1.17370 q^{79} +0.943876 q^{80} -9.13736 q^{81} -3.44758 q^{82} +4.51307 q^{83} -2.43998 q^{84} +5.34863 q^{85} +3.18527 q^{86} +6.77586 q^{87} -0.679577 q^{88} -18.7332 q^{89} -2.78773 q^{90} -6.21936 q^{91} -1.80201 q^{92} +5.08571 q^{93} -6.61137 q^{94} +4.84813 q^{95} -2.43998 q^{96} -5.15688 q^{97} -1.00000 q^{98} +2.00713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.43998	1.40872	0.704361	−	0.709842i	$-0.251234\pi$
$3$	2.43998	1.40872	0.704361	+	0.709842i	$0.251234\pi$
$4$	1.00000	0.500000
$5$	0.943876	0.422114	0.211057	−	0.977474i	$-0.432309\pi$
$5$	0.943876	0.422114	0.211057	+	0.977474i	$0.432309\pi$
$6$	−2.43998	−0.996117
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	2.95349	0.984497
$10$	−0.943876	−0.298480
$11$	0.679577	0.204900	0.102450	−	0.994738i	$-0.467332\pi$
$11$	0.679577	0.204900	0.102450	+	0.994738i	$0.467332\pi$
$12$	2.43998	0.704361
$13$	6.21936	1.72494	0.862470	−	0.506107i	$-0.168916\pi$
$13$	6.21936	1.72494	0.862470	+	0.506107i	$0.168916\pi$
$14$	1.00000	0.267261
$15$	2.30304	0.594642
$16$	1.00000	0.250000
$17$	5.66666	1.37437	0.687184	−	0.726484i	$-0.258847\pi$
$17$	5.66666	1.37437	0.687184	+	0.726484i	$0.258847\pi$
$18$	−2.95349	−0.696145
$19$	5.13641	1.17837	0.589186	−	0.807997i	$-0.299448\pi$
$19$	5.13641	1.17837	0.589186	+	0.807997i	$0.299448\pi$
$20$	0.943876	0.211057
$21$	−2.43998	−0.532447
$22$	−0.679577	−0.144886
$23$	−1.80201	−0.375746	−0.187873	−	0.982193i	$-0.560159\pi$
$23$	−1.80201	−0.375746	−0.187873	+	0.982193i	$0.560159\pi$
$24$	−2.43998	−0.498058
$25$	−4.10910	−0.821820
$26$	−6.21936	−1.21972
$27$	−0.113478	−0.0218389
$28$	−1.00000	−0.188982
$29$	2.77702	0.515679	0.257840	−	0.966188i	$-0.416989\pi$
$29$	2.77702	0.515679	0.257840	+	0.966188i	$0.416989\pi$
$30$	−2.30304	−0.420475
$31$	2.08433	0.374356	0.187178	−	0.982326i	$-0.440066\pi$
$31$	2.08433	0.374356	0.187178	+	0.982326i	$0.440066\pi$
$32$	−1.00000	−0.176777
$33$	1.65815	0.288648
$34$	−5.66666	−0.971824
$35$	−0.943876	−0.159544
$36$	2.95349	0.492249
$37$	−5.86143	−0.963614	−0.481807	−	0.876277i	$-0.660019\pi$
$37$	−5.86143	−0.963614	−0.481807	+	0.876277i	$0.660019\pi$
$38$	−5.13641	−0.833235
$39$	15.1751	2.42996
$40$	−0.943876	−0.149240
$41$	3.44758	0.538422	0.269211	−	0.963081i	$-0.413237\pi$
$41$	3.44758	0.538422	0.269211	+	0.963081i	$0.413237\pi$
$42$	2.43998	0.376497
$43$	−3.18527	−0.485750	−0.242875	−	0.970058i	$-0.578090\pi$
$43$	−3.18527	−0.485750	−0.242875	+	0.970058i	$0.578090\pi$
$44$	0.679577	0.102450
$45$	2.78773	0.415570
$46$	1.80201	0.265693
$47$	6.61137	0.964367	0.482184	−	0.876070i	$-0.339844\pi$
$47$	6.61137	0.964367	0.482184	+	0.876070i	$0.339844\pi$
$48$	2.43998	0.352180
$49$	1.00000	0.142857
$50$	4.10910	0.581114
$51$	13.8265	1.93610
$52$	6.21936	0.862470
$53$	−1.94856	−0.267656	−0.133828	−	0.991005i	$-0.542727\pi$
$53$	−1.94856	−0.267656	−0.133828	+	0.991005i	$0.542727\pi$
$54$	0.113478	0.0154424
$55$	0.641437	0.0864913
$56$	1.00000	0.133631
$57$	12.5327	1.66000
$58$	−2.77702	−0.364640
$59$	−6.17997	−0.804564	−0.402282	−	0.915516i	$-0.631783\pi$
$59$	−6.17997	−0.804564	−0.402282	+	0.915516i	$0.631783\pi$
$60$	2.30304	0.297321
$61$	10.3670	1.32736	0.663679	−	0.748017i	$-0.268994\pi$
$61$	10.3670	1.32736	0.663679	+	0.748017i	$0.268994\pi$
$62$	−2.08433	−0.264710
$63$	−2.95349	−0.372105
$64$	1.00000	0.125000
$65$	5.87031	0.728122
$66$	−1.65815	−0.204105
$67$	2.57691	0.314820	0.157410	−	0.987533i	$-0.449686\pi$
$67$	2.57691	0.314820	0.157410	+	0.987533i	$0.449686\pi$
$68$	5.66666	0.687184
$69$	−4.39688	−0.529322
$70$	0.943876	0.112815
$71$	−2.07951	−0.246793	−0.123396	−	0.992357i	$-0.539379\pi$
$71$	−2.07951	−0.246793	−0.123396	+	0.992357i	$0.539379\pi$
$72$	−2.95349	−0.348072
$73$	0.542587	0.0635050	0.0317525	−	0.999496i	$-0.489891\pi$
$73$	0.542587	0.0635050	0.0317525	+	0.999496i	$0.489891\pi$
$74$	5.86143	0.681378
$75$	−10.0261	−1.15772
$76$	5.13641	0.589186
$77$	−0.679577	−0.0774450
$78$	−15.1751	−1.71824
$79$	−1.17370	−0.132052	−0.0660258	−	0.997818i	$-0.521032\pi$
$79$	−1.17370	−0.132052	−0.0660258	+	0.997818i	$0.521032\pi$
$80$	0.943876	0.105529
$81$	−9.13736	−1.01526
$82$	−3.44758	−0.380722
$83$	4.51307	0.495374	0.247687	−	0.968840i	$-0.420330\pi$
$83$	4.51307	0.495374	0.247687	+	0.968840i	$0.420330\pi$
$84$	−2.43998	−0.266223
$85$	5.34863	0.580140
$86$	3.18527	0.343477
$87$	6.77586	0.726449
$88$	−0.679577	−0.0724432
$89$	−18.7332	−1.98571	−0.992855	−	0.119325i	$-0.961927\pi$
$89$	−18.7332	−1.98571	−0.992855	+	0.119325i	$0.961927\pi$
$90$	−2.78773	−0.293853
$91$	−6.21936	−0.651966
$92$	−1.80201	−0.187873
$93$	5.08571	0.527364
$94$	−6.61137	−0.681911
$95$	4.84813	0.497408
$96$	−2.43998	−0.249029
$97$	−5.15688	−0.523602	−0.261801	−	0.965122i	$-0.584316\pi$
$97$	−5.15688	−0.523602	−0.261801	+	0.965122i	$0.584316\pi$
$98$	−1.00000	−0.101015
$99$	2.00713	0.201724
$100$	−4.10910	−0.410910
$101$	−5.61400	−0.558613	−0.279307	−	0.960202i	$-0.590105\pi$
$101$	−5.61400	−0.558613	−0.279307	+	0.960202i	$0.590105\pi$
$102$	−13.8265	−1.36903
$103$	−5.61145	−0.552912	−0.276456	−	0.961027i	$-0.589160\pi$
$103$	−5.61145	−0.552912	−0.276456	+	0.961027i	$0.589160\pi$
$104$	−6.21936	−0.609859
$105$	−2.30304	−0.224753
$106$	1.94856	0.189261
$107$	10.2691	0.992754	0.496377	−	0.868107i	$-0.334663\pi$
$107$	10.2691	0.992754	0.496377	+	0.868107i	$0.334663\pi$
$108$	−0.113478	−0.0109194
$109$	2.83932	0.271958	0.135979	−	0.990712i	$-0.456582\pi$
$109$	2.83932	0.271958	0.135979	+	0.990712i	$0.456582\pi$
$110$	−0.641437	−0.0611586
$111$	−14.3018	−1.35746
$112$	−1.00000	−0.0944911
$113$	12.4677	1.17287	0.586433	−	0.809998i	$-0.300532\pi$
$113$	12.4677	1.17287	0.586433	+	0.809998i	$0.300532\pi$
$114$	−12.5327	−1.17380
$115$	−1.70088	−0.158608
$116$	2.77702	0.257840
$117$	18.3688	1.69820
$118$	6.17997	0.568912
$119$	−5.66666	−0.519462
$120$	−2.30304	−0.210238
$121$	−10.5382	−0.958016
$122$	−10.3670	−0.938584
$123$	8.41203	0.758487
$124$	2.08433	0.187178
$125$	−8.59786	−0.769016
$126$	2.95349	0.263118
$127$	−14.4105	−1.27872	−0.639361	−	0.768907i	$-0.720801\pi$
$127$	−14.4105	−1.27872	−0.639361	+	0.768907i	$0.720801\pi$
$128$	−1.00000	−0.0883883
$129$	−7.77200	−0.684286
$130$	−5.87031	−0.514860
$131$	12.6756	1.10747	0.553736	−	0.832692i	$-0.313202\pi$
$131$	12.6756	1.10747	0.553736	+	0.832692i	$0.313202\pi$
$132$	1.65815	0.144324
$133$	−5.13641	−0.445383
$134$	−2.57691	−0.222611
$135$	−0.107109	−0.00921851
$136$	−5.66666	−0.485912
$137$	5.06561	0.432784	0.216392	−	0.976307i	$-0.430571\pi$
$137$	5.06561	0.432784	0.216392	+	0.976307i	$0.430571\pi$
$138$	4.39688	0.374287
$139$	−1.78094	−0.151057	−0.0755285	−	0.997144i	$-0.524064\pi$
$139$	−1.78094	−0.151057	−0.0755285	+	0.997144i	$0.524064\pi$
$140$	−0.943876	−0.0797721
$141$	16.1316	1.35853
$142$	2.07951	0.174509
$143$	4.22654	0.353441
$144$	2.95349	0.246124
$145$	2.62116	0.217676
$146$	−0.542587	−0.0449048
$147$	2.43998	0.201246
$148$	−5.86143	−0.481807
$149$	8.92807	0.731416	0.365708	−	0.930730i	$-0.380827\pi$
$149$	8.92807	0.731416	0.365708	+	0.930730i	$0.380827\pi$
$150$	10.0261	0.818628
$151$	14.2678	1.16110	0.580549	−	0.814225i	$-0.302838\pi$
$151$	14.2678	1.16110	0.580549	+	0.814225i	$0.302838\pi$
$152$	−5.13641	−0.416618
$153$	16.7364	1.35306
$154$	0.679577	0.0547619
$155$	1.96735	0.158021
$156$	15.1751	1.21498
$157$	−12.4671	−0.994980	−0.497490	−	0.867470i	$-0.665745\pi$
$157$	−12.4671	−0.994980	−0.497490	+	0.867470i	$0.665745\pi$
$158$	1.17370	0.0933746
$159$	−4.75445	−0.377053
$160$	−0.943876	−0.0746200
$161$	1.80201	0.142019
$162$	9.13736	0.717899
$163$	−4.35674	−0.341246	−0.170623	−	0.985336i	$-0.554578\pi$
$163$	−4.35674	−0.341246	−0.170623	+	0.985336i	$0.554578\pi$
$164$	3.44758	0.269211
$165$	1.56509	0.121842
$166$	−4.51307	−0.350282
$167$	−8.01306	−0.620069	−0.310034	−	0.950725i	$-0.600341\pi$
$167$	−8.01306	−0.620069	−0.310034	+	0.950725i	$0.600341\pi$
$168$	2.43998	0.188248
$169$	25.6805	1.97542
$170$	−5.34863	−0.410221
$171$	15.1703	1.16011
$172$	−3.18527	−0.242875
$173$	9.77826	0.743428	0.371714	−	0.928347i	$-0.378770\pi$
$173$	9.77826	0.743428	0.371714	+	0.928347i	$0.378770\pi$
$174$	−6.77586	−0.513677
$175$	4.10910	0.310619
$176$	0.679577	0.0512251
$177$	−15.0790	−1.13341
$178$	18.7332	1.40411
$179$	7.15064	0.534464	0.267232	−	0.963632i	$-0.413891\pi$
$179$	7.15064	0.534464	0.267232	+	0.963632i	$0.413891\pi$
$180$	2.78773	0.207785
$181$	−12.8211	−0.952984	−0.476492	−	0.879179i	$-0.658092\pi$
$181$	−12.8211	−0.952984	−0.476492	+	0.879179i	$0.658092\pi$
$182$	6.21936	0.461010
$183$	25.2952	1.86988
$184$	1.80201	0.132846
$185$	−5.53247	−0.406755
$186$	−5.08571	−0.372903
$187$	3.85094	0.281608
$188$	6.61137	0.482184
$189$	0.113478	0.00825433
$190$	−4.84813	−0.351721
$191$	18.0129	1.30337	0.651683	−	0.758491i	$-0.274063\pi$
$191$	18.0129	1.30337	0.651683	+	0.758491i	$0.274063\pi$
$192$	2.43998	0.176090
$193$	15.1617	1.09136	0.545680	−	0.837993i	$-0.316271\pi$
$193$	15.1617	1.09136	0.545680	+	0.837993i	$0.316271\pi$
$194$	5.15688	0.370243
$195$	14.3234	1.02572
$196$	1.00000	0.0714286
$197$	−21.4802	−1.53040	−0.765202	−	0.643790i	$-0.777361\pi$
$197$	−21.4802	−1.53040	−0.765202	+	0.643790i	$0.777361\pi$
$198$	−2.00713	−0.142640
$199$	10.9980	0.779626	0.389813	−	0.920894i	$-0.372540\pi$
$199$	10.9980	0.779626	0.389813	+	0.920894i	$0.372540\pi$
$200$	4.10910	0.290557
$201$	6.28761	0.443494
$202$	5.61400	0.394999
$203$	−2.77702	−0.194908
$204$	13.8265	0.968051
$205$	3.25409	0.227276
$206$	5.61145	0.390968
$207$	−5.32224	−0.369921
$208$	6.21936	0.431235
$209$	3.49059	0.241449
$210$	2.30304	0.158925
$211$	8.39451	0.577902	0.288951	−	0.957344i	$-0.406694\pi$
$211$	8.39451	0.577902	0.288951	+	0.957344i	$0.406694\pi$
$212$	−1.94856	−0.133828
$213$	−5.07396	−0.347662
$214$	−10.2691	−0.701983
$215$	−3.00650	−0.205042
$216$	0.113478	0.00772122
$217$	−2.08433	−0.141493
$218$	−2.83932	−0.192303
$219$	1.32390	0.0894608
$220$	0.641437	0.0432457
$221$	35.2430	2.37070
$222$	14.3018	0.959872
$223$	14.9872	1.00362	0.501810	−	0.864978i	$-0.332668\pi$
$223$	14.9872	1.00362	0.501810	+	0.864978i	$0.332668\pi$
$224$	1.00000	0.0668153
$225$	−12.1362	−0.809079
$226$	−12.4677	−0.829341
$227$	12.4708	0.827718	0.413859	−	0.910341i	$-0.364181\pi$
$227$	12.4708	0.827718	0.413859	+	0.910341i	$0.364181\pi$
$228$	12.5327	0.830000
$229$	−6.92575	−0.457666	−0.228833	−	0.973466i	$-0.573491\pi$
$229$	−6.92575	−0.457666	−0.228833	+	0.973466i	$0.573491\pi$
$230$	1.70088	0.112153
$231$	−1.65815	−0.109099
$232$	−2.77702	−0.182320
$233$	−12.4395	−0.814939	−0.407470	−	0.913219i	$-0.633589\pi$
$233$	−12.4395	−0.814939	−0.407470	+	0.913219i	$0.633589\pi$
$234$	−18.3688	−1.20081
$235$	6.24031	0.407073
$236$	−6.17997	−0.402282
$237$	−2.86380	−0.186024
$238$	5.66666	0.367315
$239$	2.89225	0.187084	0.0935420	−	0.995615i	$-0.470181\pi$
$239$	2.89225	0.187084	0.0935420	+	0.995615i	$0.470181\pi$
$240$	2.30304	0.148660
$241$	−27.1587	−1.74945	−0.874724	−	0.484621i	$-0.838957\pi$
$241$	−27.1587	−1.74945	−0.874724	+	0.484621i	$0.838957\pi$
$242$	10.5382	0.677420
$243$	−21.9545	−1.40838
$244$	10.3670	0.663679
$245$	0.943876	0.0603020
$246$	−8.41203	−0.536331
$247$	31.9452	2.03262
$248$	−2.08433	−0.132355
$249$	11.0118	0.697844
$250$	8.59786	0.543776
$251$	−3.00749	−0.189831	−0.0949154	−	0.995485i	$-0.530258\pi$
$251$	−3.00749	−0.189831	−0.0949154	+	0.995485i	$0.530258\pi$
$252$	−2.95349	−0.186053
$253$	−1.22461	−0.0769905
$254$	14.4105	0.904193
$255$	13.0505	0.817256
$256$	1.00000	0.0625000
$257$	−19.6209	−1.22392	−0.611959	−	0.790889i	$-0.709618\pi$
$257$	−19.6209	−1.22392	−0.611959	+	0.790889i	$0.709618\pi$
$258$	7.77200	0.483863
$259$	5.86143	0.364212
$260$	5.87031	0.364061
$261$	8.20190	0.507685
$262$	−12.6756	−0.783101
$263$	−6.13060	−0.378029	−0.189014	−	0.981974i	$-0.560529\pi$
$263$	−6.13060	−0.378029	−0.189014	+	0.981974i	$0.560529\pi$
$264$	−1.65815	−0.102052
$265$	−1.83920	−0.112981
$266$	5.13641	0.314933
$267$	−45.7085	−2.79731
$268$	2.57691	0.157410
$269$	−2.40728	−0.146774	−0.0733872	−	0.997304i	$-0.523381\pi$
$269$	−2.40728	−0.146774	−0.0733872	+	0.997304i	$0.523381\pi$
$270$	0.107109	0.00651847
$271$	19.7243	1.19817	0.599084	−	0.800687i	$-0.295532\pi$
$271$	19.7243	1.19817	0.599084	+	0.800687i	$0.295532\pi$
$272$	5.66666	0.343592
$273$	−15.1751	−0.918439
$274$	−5.06561	−0.306025
$275$	−2.79245	−0.168391
$276$	−4.39688	−0.264661
$277$	5.25613	0.315810	0.157905	−	0.987454i	$-0.449526\pi$
$277$	5.25613	0.315810	0.157905	+	0.987454i	$0.449526\pi$
$278$	1.78094	0.106813
$279$	6.15605	0.368553
$280$	0.943876	0.0564074
$281$	27.2745	1.62706	0.813529	−	0.581524i	$-0.197543\pi$
$281$	27.2745	1.62706	0.813529	+	0.581524i	$0.197543\pi$
$282$	−16.1316	−0.960622
$283$	20.7835	1.23545	0.617725	−	0.786394i	$-0.288054\pi$
$283$	20.7835	1.23545	0.617725	+	0.786394i	$0.288054\pi$
$284$	−2.07951	−0.123396
$285$	11.8293	0.700710
$286$	−4.22654	−0.249920
$287$	−3.44758	−0.203504
$288$	−2.95349	−0.174036
$289$	15.1111	0.888886
$290$	−2.62116	−0.153920
$291$	−12.5827	−0.737610
$292$	0.542587	0.0317525
$293$	−15.2345	−0.890011	−0.445005	−	0.895528i	$-0.646798\pi$
$293$	−15.2345	−0.890011	−0.445005	+	0.895528i	$0.646798\pi$
$294$	−2.43998	−0.142302
$295$	−5.83313	−0.339618
$296$	5.86143	0.340689
$297$	−0.0771172	−0.00447480
$298$	−8.92807	−0.517189
$299$	−11.2074	−0.648140
$300$	−10.0261	−0.578858
$301$	3.18527	0.183596
$302$	−14.2678	−0.821020
$303$	−13.6980	−0.786931
$304$	5.13641	0.294593
$305$	9.78516	0.560297
$306$	−16.7364	−0.956759
$307$	−14.5034	−0.827750	−0.413875	−	0.910334i	$-0.635825\pi$
$307$	−14.5034	−0.827750	−0.413875	+	0.910334i	$0.635825\pi$
$308$	−0.679577	−0.0387225
$309$	−13.6918	−0.778899
$310$	−1.96735	−0.111738
$311$	30.7242	1.74221	0.871104	−	0.491099i	$-0.163405\pi$
$311$	30.7242	1.74221	0.871104	+	0.491099i	$0.163405\pi$
$312$	−15.1751	−0.859121
$313$	6.23638	0.352501	0.176251	−	0.984345i	$-0.443603\pi$
$313$	6.23638	0.352501	0.176251	+	0.984345i	$0.443603\pi$
$314$	12.4671	0.703557
$315$	−2.78773	−0.157071
$316$	−1.17370	−0.0660258
$317$	21.7014	1.21887	0.609436	−	0.792835i	$-0.291396\pi$
$317$	21.7014	1.21887	0.609436	+	0.792835i	$0.291396\pi$
$318$	4.75445	0.266616
$319$	1.88720	0.105663
$320$	0.943876	0.0527643
$321$	25.0564	1.39851
$322$	−1.80201	−0.100422
$323$	29.1063	1.61952
$324$	−9.13736	−0.507631
$325$	−25.5560	−1.41759
$326$	4.35674	0.241297
$327$	6.92789	0.383113
$328$	−3.44758	−0.190361
$329$	−6.61137	−0.364497
$330$	−1.56509	−0.0861555
$331$	−22.0802	−1.21364	−0.606818	−	0.794841i	$-0.707554\pi$
$331$	−22.0802	−1.21364	−0.606818	+	0.794841i	$0.707554\pi$
$332$	4.51307	0.247687
$333$	−17.3117	−0.948675
$334$	8.01306	0.438455
$335$	2.43229	0.132890
$336$	−2.43998	−0.133112
$337$	−15.2031	−0.828167	−0.414084	−	0.910239i	$-0.635898\pi$
$337$	−15.2031	−0.828167	−0.414084	+	0.910239i	$0.635898\pi$
$338$	−25.6805	−1.39683
$339$	30.4210	1.65224
$340$	5.34863	0.290070
$341$	1.41646	0.0767057
$342$	−15.1703	−0.820318
$343$	−1.00000	−0.0539949
$344$	3.18527	0.171738
$345$	−4.15011	−0.223434
$346$	−9.77826	−0.525683
$347$	4.09031	0.219579	0.109790	−	0.993955i	$-0.464982\pi$
$347$	4.09031	0.219579	0.109790	+	0.993955i	$0.464982\pi$
$348$	6.77586	0.363224
$349$	−29.2738	−1.56699	−0.783496	−	0.621397i	$-0.786565\pi$
$349$	−29.2738	−1.56699	−0.783496	+	0.621397i	$0.786565\pi$
$350$	−4.10910	−0.219641
$351$	−0.705762	−0.0376708
$352$	−0.679577	−0.0362216
$353$	−1.68651	−0.0897637	−0.0448819	−	0.998992i	$-0.514291\pi$
$353$	−1.68651	−0.0897637	−0.0448819	+	0.998992i	$0.514291\pi$
$354$	15.0790	0.801439
$355$	−1.96280	−0.104175
$356$	−18.7332	−0.992855
$357$	−13.8265	−0.731778
$358$	−7.15064	−0.377923
$359$	2.72316	0.143723	0.0718614	−	0.997415i	$-0.477106\pi$
$359$	2.72316	0.143723	0.0718614	+	0.997415i	$0.477106\pi$
$360$	−2.78773	−0.146926
$361$	7.38269	0.388563
$362$	12.8211	0.673862
$363$	−25.7129	−1.34958
$364$	−6.21936	−0.325983
$365$	0.512135	0.0268064
$366$	−25.2952	−1.32220
$367$	−17.2015	−0.897909	−0.448955	−	0.893555i	$-0.648203\pi$
$367$	−17.2015	−0.897909	−0.448955	+	0.893555i	$0.648203\pi$
$368$	−1.80201	−0.0939365
$369$	10.1824	0.530075
$370$	5.53247	0.287619
$371$	1.94856	0.101164
$372$	5.08571	0.263682
$373$	−13.9913	−0.724444	−0.362222	−	0.932092i	$-0.617982\pi$
$373$	−13.9913	−0.724444	−0.362222	+	0.932092i	$0.617982\pi$
$374$	−3.85094	−0.199127
$375$	−20.9786	−1.08333
$376$	−6.61137	−0.340955
$377$	17.2713	0.889516
$378$	−0.113478	−0.00583669
$379$	10.0002	0.513674	0.256837	−	0.966455i	$-0.417320\pi$
$379$	10.0002	0.513674	0.256837	+	0.966455i	$0.417320\pi$
$380$	4.84813	0.248704
$381$	−35.1612	−1.80136
$382$	−18.0129	−0.921619
$383$	27.0124	1.38027	0.690133	−	0.723682i	$-0.257552\pi$
$383$	27.0124	1.38027	0.690133	+	0.723682i	$0.257552\pi$
$384$	−2.43998	−0.124515
$385$	−0.641437	−0.0326907
$386$	−15.1617	−0.771709
$387$	−9.40768	−0.478219
$388$	−5.15688	−0.261801
$389$	20.8651	1.05790	0.528951	−	0.848652i	$-0.322586\pi$
$389$	20.8651	1.05790	0.528951	+	0.848652i	$0.322586\pi$
$390$	−14.3234	−0.725295
$391$	−10.2114	−0.516413
$392$	−1.00000	−0.0505076
$393$	30.9282	1.56012
$394$	21.4802	1.08216
$395$	−1.10783	−0.0557409
$396$	2.00713	0.100862
$397$	16.7013	0.838212	0.419106	−	0.907937i	$-0.362343\pi$
$397$	16.7013	0.838212	0.419106	+	0.907937i	$0.362343\pi$
$398$	−10.9980	−0.551279
$399$	−12.5327	−0.627421
$400$	−4.10910	−0.205455
$401$	−5.35935	−0.267633	−0.133817	−	0.991006i	$-0.542723\pi$
$401$	−5.35935	−0.267633	−0.133817	+	0.991006i	$0.542723\pi$
$402$	−6.28761	−0.313597
$403$	12.9632	0.645742
$404$	−5.61400	−0.279307
$405$	−8.62454	−0.428557
$406$	2.77702	0.137821
$407$	−3.98330	−0.197445
$408$	−13.8265	−0.684515
$409$	32.2009	1.59223	0.796116	−	0.605144i	$-0.206885\pi$
$409$	32.2009	1.59223	0.796116	+	0.605144i	$0.206885\pi$
$410$	−3.25409	−0.160708
$411$	12.3600	0.609672
$412$	−5.61145	−0.276456
$413$	6.17997	0.304097
$414$	5.32224	0.261574
$415$	4.25978	0.209104
$416$	−6.21936	−0.304929
$417$	−4.34544	−0.212797
$418$	−3.49059	−0.170730
$419$	−17.7818	−0.868698	−0.434349	−	0.900745i	$-0.643022\pi$
$419$	−17.7818	−0.868698	−0.434349	+	0.900745i	$0.643022\pi$
$420$	−2.30304	−0.112377
$421$	−4.94597	−0.241052	−0.120526	−	0.992710i	$-0.538458\pi$
$421$	−4.94597	−0.241052	−0.120526	+	0.992710i	$0.538458\pi$
$422$	−8.39451	−0.408638
$423$	19.5266	0.949417
$424$	1.94856	0.0946306
$425$	−23.2849	−1.12948
$426$	5.07396	0.245834
$427$	−10.3670	−0.501694
$428$	10.2691	0.496377
$429$	10.3127	0.497900
$430$	3.00650	0.144986
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−0.113478	−0.00545972
$433$	−15.4958	−0.744681	−0.372341	−	0.928096i	$-0.621445\pi$
$433$	−15.4958	−0.744681	−0.372341	+	0.928096i	$0.621445\pi$
$434$	2.08433	0.100051
$435$	6.39558	0.306644
$436$	2.83932	0.135979
$437$	−9.25588	−0.442769
$438$	−1.32390	−0.0632584
$439$	−6.45344	−0.308006	−0.154003	−	0.988070i	$-0.549217\pi$
$439$	−6.45344	−0.308006	−0.154003	+	0.988070i	$0.549217\pi$
$440$	−0.641437	−0.0305793
$441$	2.95349	0.140642
$442$	−35.2430	−1.67634
$443$	11.5683	0.549624	0.274812	−	0.961498i	$-0.411384\pi$
$443$	11.5683	0.549624	0.274812	+	0.961498i	$0.411384\pi$
$444$	−14.3018	−0.678732
$445$	−17.6818	−0.838197
$446$	−14.9872	−0.709667
$447$	21.7843	1.03036
$448$	−1.00000	−0.0472456
$449$	1.04394	0.0492668	0.0246334	−	0.999697i	$-0.492158\pi$
$449$	1.04394	0.0492668	0.0246334	+	0.999697i	$0.492158\pi$
$450$	12.1362	0.572105
$451$	2.34290	0.110323
$452$	12.4677	0.586433
$453$	34.8131	1.63566
$454$	−12.4708	−0.585285
$455$	−5.87031	−0.275204
$456$	−12.5327	−0.586899
$457$	−25.9981	−1.21614	−0.608069	−	0.793884i	$-0.708056\pi$
$457$	−25.9981	−1.21614	−0.608069	+	0.793884i	$0.708056\pi$
$458$	6.92575	0.323619
$459$	−0.643043	−0.0300147
$460$	−1.70088	−0.0793039
$461$	−26.0485	−1.21320	−0.606601	−	0.795007i	$-0.707467\pi$
$461$	−26.0485	−1.21320	−0.606601	+	0.795007i	$0.707467\pi$
$462$	1.65815	0.0771443
$463$	−9.47750	−0.440457	−0.220228	−	0.975448i	$-0.570680\pi$
$463$	−9.47750	−0.440457	−0.220228	+	0.975448i	$0.570680\pi$
$464$	2.77702	0.128920
$465$	4.80028	0.222608
$466$	12.4395	0.576249
$467$	0.719422	0.0332909	0.0166454	−	0.999861i	$-0.494701\pi$
$467$	0.719422	0.0332909	0.0166454	+	0.999861i	$0.494701\pi$
$468$	18.3688	0.849100
$469$	−2.57691	−0.118991
$470$	−6.24031	−0.287844
$471$	−30.4194	−1.40165
$472$	6.17997	0.284456
$473$	−2.16464	−0.0995302
$474$	2.86380	0.131539
$475$	−21.1060	−0.968410
$476$	−5.66666	−0.259731
$477$	−5.75507	−0.263506
$478$	−2.89225	−0.132288
$479$	24.5385	1.12119	0.560596	−	0.828089i	$-0.310572\pi$
$479$	24.5385	1.12119	0.560596	+	0.828089i	$0.310572\pi$
$480$	−2.30304	−0.105119
$481$	−36.4544	−1.66218
$482$	27.1587	1.23705
$483$	4.39688	0.200065
$484$	−10.5382	−0.479008
$485$	−4.86746	−0.221020
$486$	21.9545	0.995877
$487$	17.5916	0.797150	0.398575	−	0.917136i	$-0.369505\pi$
$487$	17.5916	0.797150	0.398575	+	0.917136i	$0.369505\pi$
$488$	−10.3670	−0.469292
$489$	−10.6303	−0.480721
$490$	−0.943876	−0.0426400
$491$	−15.0733	−0.680250	−0.340125	−	0.940380i	$-0.610469\pi$
$491$	−15.0733	−0.680250	−0.340125	+	0.940380i	$0.610469\pi$
$492$	8.41203	0.379244
$493$	15.7364	0.708733
$494$	−31.9452	−1.43728
$495$	1.89448	0.0851505
$496$	2.08433	0.0935891
$497$	2.07951	0.0932788
$498$	−11.0118	−0.493450
$499$	−1.97964	−0.0886209	−0.0443105	−	0.999018i	$-0.514109\pi$
$499$	−1.97964	−0.0886209	−0.0443105	+	0.999018i	$0.514109\pi$
$500$	−8.59786	−0.384508
$501$	−19.5517	−0.873505
$502$	3.00749	0.134231
$503$	−18.4961	−0.824698	−0.412349	−	0.911026i	$-0.635292\pi$
$503$	−18.4961	−0.824698	−0.412349	+	0.911026i	$0.635292\pi$
$504$	2.95349	0.131559
$505$	−5.29892	−0.235799
$506$	1.22461	0.0544405
$507$	62.6598	2.78282
$508$	−14.4105	−0.639361
$509$	24.0356	1.06536	0.532681	−	0.846316i	$-0.321185\pi$
$509$	24.0356	1.06536	0.532681	+	0.846316i	$0.321185\pi$
$510$	−13.0505	−0.577887
$511$	−0.542587	−0.0240026
$512$	−1.00000	−0.0441942
$513$	−0.582871	−0.0257344
$514$	19.6209	0.865441
$515$	−5.29651	−0.233392
$516$	−7.77200	−0.342143
$517$	4.49294	0.197599
$518$	−5.86143	−0.257537
$519$	23.8587	1.04728
$520$	−5.87031	−0.257430
$521$	−7.78795	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$521$	−7.78795	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$522$	−8.20190	−0.358987
$523$	28.2658	1.23598	0.617989	−	0.786186i	$-0.287947\pi$
$523$	28.2658	1.23598	0.617989	+	0.786186i	$0.287947\pi$
$524$	12.6756	0.553736
$525$	10.0261	0.437575
$526$	6.13060	0.267307
$527$	11.8112	0.514503
$528$	1.65815	0.0721619
$529$	−19.7527	−0.858815
$530$	1.83920	0.0798899
$531$	−18.2525	−0.792091
$532$	−5.13641	−0.222692
$533$	21.4418	0.928747
$534$	45.7085	1.97800
$535$	9.69279	0.419056
$536$	−2.57691	−0.111306
$537$	17.4474	0.752911
$538$	2.40728	0.103785
$539$	0.679577	0.0292715
$540$	−0.107109	−0.00460926
$541$	−18.6563	−0.802096	−0.401048	−	0.916057i	$-0.631354\pi$
$541$	−18.6563	−0.802096	−0.401048	+	0.916057i	$0.631354\pi$
$542$	−19.7243	−0.847232
$543$	−31.2832	−1.34249
$544$	−5.66666	−0.242956
$545$	2.67997	0.114797
$546$	15.1751	0.649435
$547$	24.3635	1.04171	0.520854	−	0.853646i	$-0.325614\pi$
$547$	24.3635	1.04171	0.520854	+	0.853646i	$0.325614\pi$
$548$	5.06561	0.216392
$549$	30.6188	1.30678
$550$	2.79245	0.119070
$551$	14.2639	0.607663
$552$	4.39688	0.187143
$553$	1.17370	0.0499108
$554$	−5.25613	−0.223312
$555$	−13.4991	−0.573005
$556$	−1.78094	−0.0755285
$557$	−1.84796	−0.0783007	−0.0391504	−	0.999233i	$-0.512465\pi$
$557$	−1.84796	−0.0783007	−0.0391504	+	0.999233i	$0.512465\pi$
$558$	−6.15605	−0.260606
$559$	−19.8104	−0.837889
$560$	−0.943876	−0.0398861
$561$	9.39620	0.396708
$562$	−27.2745	−1.15050
$563$	−3.66461	−0.154445	−0.0772224	−	0.997014i	$-0.524605\pi$
$563$	−3.66461	−0.154445	−0.0772224	+	0.997014i	$0.524605\pi$
$564$	16.1316	0.679263
$565$	11.7680	0.495083
$566$	−20.7835	−0.873596
$567$	9.13736	0.383733
$568$	2.07951	0.0872543
$569$	−35.6788	−1.49573	−0.747867	−	0.663848i	$-0.768922\pi$
$569$	−35.6788	−1.49573	−0.747867	+	0.663848i	$0.768922\pi$
$570$	−11.8293	−0.495477
$571$	−39.2439	−1.64230	−0.821152	−	0.570709i	$-0.806668\pi$
$571$	−39.2439	−1.64230	−0.821152	+	0.570709i	$0.806668\pi$
$572$	4.22654	0.176720
$573$	43.9510	1.83608
$574$	3.44758	0.143899
$575$	7.40465	0.308795
$576$	2.95349	0.123062
$577$	25.4158	1.05807	0.529037	−	0.848599i	$-0.322553\pi$
$577$	25.4158	1.05807	0.529037	+	0.848599i	$0.322553\pi$
$578$	−15.1111	−0.628537
$579$	36.9941	1.53742
$580$	2.62116	0.108838
$581$	−4.51307	−0.187234
$582$	12.5827	0.521569
$583$	−1.32420	−0.0548428
$584$	−0.542587	−0.0224524
$585$	17.3379	0.716834
$586$	15.2345	0.629333
$587$	−32.1039	−1.32507	−0.662534	−	0.749032i	$-0.730519\pi$
$587$	−32.1039	−1.32507	−0.662534	+	0.749032i	$0.730519\pi$
$588$	2.43998	0.100623
$589$	10.7060	0.441131
$590$	5.83313	0.240146
$591$	−52.4113	−2.15591
$592$	−5.86143	−0.240903
$593$	40.7901	1.67505	0.837525	−	0.546400i	$-0.184002\pi$
$593$	40.7901	1.67505	0.837525	+	0.546400i	$0.184002\pi$
$594$	0.0771172	0.00316416
$595$	−5.34863	−0.219272
$596$	8.92807	0.365708
$597$	26.8348	1.09828
$598$	11.2074	0.458304
$599$	38.8777	1.58850	0.794249	−	0.607592i	$-0.207865\pi$
$599$	38.8777	1.58850	0.794249	+	0.607592i	$0.207865\pi$
$600$	10.0261	0.409314
$601$	−11.0149	−0.449306	−0.224653	−	0.974439i	$-0.572125\pi$
$601$	−11.0149	−0.449306	−0.224653	+	0.974439i	$0.572125\pi$
$602$	−3.18527	−0.129822
$603$	7.61089	0.309939
$604$	14.2678	0.580549
$605$	−9.94673	−0.404392
$606$	13.6980	0.556444
$607$	−1.47638	−0.0599246	−0.0299623	−	0.999551i	$-0.509539\pi$
$607$	−1.47638	−0.0599246	−0.0299623	+	0.999551i	$0.509539\pi$
$608$	−5.13641	−0.208309
$609$	−6.77586	−0.274572
$610$	−9.78516	−0.396190
$611$	41.1185	1.66348
$612$	16.7364	0.676531
$613$	37.0191	1.49519	0.747593	−	0.664157i	$-0.231209\pi$
$613$	37.0191	1.49519	0.747593	+	0.664157i	$0.231209\pi$
$614$	14.5034	0.585308
$615$	7.93992	0.320168
$616$	0.679577	0.0273810
$617$	−34.1976	−1.37675	−0.688373	−	0.725357i	$-0.741675\pi$
$617$	−34.1976	−1.37675	−0.688373	+	0.725357i	$0.741675\pi$
$618$	13.6918	0.550765
$619$	−11.0959	−0.445984	−0.222992	−	0.974820i	$-0.571582\pi$
$619$	−11.0959	−0.445984	−0.222992	+	0.974820i	$0.571582\pi$
$620$	1.96735	0.0790106
$621$	0.204489	0.00820588
$622$	−30.7242	−1.23193
$623$	18.7332	0.750528
$624$	15.1751	0.607490
$625$	12.4302	0.497207
$626$	−6.23638	−0.249256
$627$	8.51696	0.340134
$628$	−12.4671	−0.497490
$629$	−33.2148	−1.32436
$630$	2.78773	0.111066
$631$	−19.0489	−0.758324	−0.379162	−	0.925330i	$-0.623788\pi$
$631$	−19.0489	−0.758324	−0.379162	+	0.925330i	$0.623788\pi$
$632$	1.17370	0.0466873
$633$	20.4824	0.814103
$634$	−21.7014	−0.861872
$635$	−13.6017	−0.539767
$636$	−4.75445	−0.188526
$637$	6.21936	0.246420
$638$	−1.88720	−0.0747149
$639$	−6.14182	−0.242967
$640$	−0.943876	−0.0373100
$641$	−46.3839	−1.83206	−0.916028	−	0.401115i	$-0.868623\pi$
$641$	−46.3839	−1.83206	−0.916028	+	0.401115i	$0.868623\pi$
$642$	−25.0564	−0.988899
$643$	−40.5362	−1.59859	−0.799296	−	0.600937i	$-0.794794\pi$
$643$	−40.5362	−1.59859	−0.799296	+	0.600937i	$0.794794\pi$
$644$	1.80201	0.0710093
$645$	−7.33580	−0.288847
$646$	−29.1063	−1.14517
$647$	−41.6943	−1.63917	−0.819586	−	0.572957i	$-0.805796\pi$
$647$	−41.6943	−1.63917	−0.819586	+	0.572957i	$0.805796\pi$
$648$	9.13736	0.358949
$649$	−4.19977	−0.164855
$650$	25.5560	1.00239
$651$	−5.08571	−0.199325
$652$	−4.35674	−0.170623
$653$	−10.1129	−0.395750	−0.197875	−	0.980227i	$-0.563404\pi$
$653$	−10.1129	−0.395750	−0.197875	+	0.980227i	$0.563404\pi$
$654$	−6.92789	−0.270902
$655$	11.9642	0.467480
$656$	3.44758	0.134606
$657$	1.60253	0.0625205
$658$	6.61137	0.257738
$659$	17.2558	0.672192	0.336096	−	0.941828i	$-0.390893\pi$
$659$	17.2558	0.672192	0.336096	+	0.941828i	$0.390893\pi$
$660$	1.56509	0.0609211
$661$	6.89219	0.268075	0.134037	−	0.990976i	$-0.457206\pi$
$661$	6.89219	0.268075	0.134037	+	0.990976i	$0.457206\pi$
$662$	22.0802	0.858171
$663$	85.9922	3.33966
$664$	−4.51307	−0.175141
$665$	−4.84813	−0.188003
$666$	17.3117	0.670815
$667$	−5.00423	−0.193764
$668$	−8.01306	−0.310034
$669$	36.5685	1.41382
$670$	−2.43229	−0.0939674
$671$	7.04518	0.271976
$672$	2.43998	0.0941242
$673$	−40.1127	−1.54623	−0.773115	−	0.634266i	$-0.781302\pi$
$673$	−40.1127	−1.54623	−0.773115	+	0.634266i	$0.781302\pi$
$674$	15.2031	0.585603
$675$	0.466293	0.0179476
$676$	25.6805	0.987711
$677$	30.7406	1.18146	0.590728	−	0.806871i	$-0.298841\pi$
$677$	30.7406	1.18146	0.590728	+	0.806871i	$0.298841\pi$
$678$	−30.4210	−1.16831
$679$	5.15688	0.197903
$680$	−5.34863	−0.205111
$681$	30.4286	1.16602
$682$	−1.41646	−0.0542391
$683$	−36.6281	−1.40154	−0.700768	−	0.713389i	$-0.747159\pi$
$683$	−36.6281	−1.40154	−0.700768	+	0.713389i	$0.747159\pi$
$684$	15.1703	0.580053
$685$	4.78131	0.182684
$686$	1.00000	0.0381802
$687$	−16.8987	−0.644725
$688$	−3.18527	−0.121437
$689$	−12.1188	−0.461690
$690$	4.15011	0.157992
$691$	31.2180	1.18759	0.593794	−	0.804617i	$-0.297629\pi$
$691$	31.2180	1.18759	0.593794	+	0.804617i	$0.297629\pi$
$692$	9.77826	0.371714
$693$	−2.00713	−0.0762444
$694$	−4.09031	−0.155266
$695$	−1.68098	−0.0637633
$696$	−6.77586	−0.256838
$697$	19.5363	0.739990
$698$	29.2738	1.10803
$699$	−30.3521	−1.14802
$700$	4.10910	0.155309
$701$	−15.0291	−0.567640	−0.283820	−	0.958878i	$-0.591602\pi$
$701$	−15.0291	−0.567640	−0.283820	+	0.958878i	$0.591602\pi$
$702$	0.705762	0.0266373
$703$	−30.1067	−1.13550
$704$	0.679577	0.0256125
$705$	15.2262	0.573453
$706$	1.68651	0.0634725
$707$	5.61400	0.211136
$708$	−15.0790	−0.566703
$709$	45.8560	1.72216	0.861079	−	0.508470i	$-0.169789\pi$
$709$	45.8560	1.72216	0.861079	+	0.508470i	$0.169789\pi$
$710$	1.96280	0.0736626
$711$	−3.46652	−0.130004
$712$	18.7332	0.702055
$713$	−3.75599	−0.140663
$714$	13.8265	0.517445
$715$	3.98933	0.149192
$716$	7.15064	0.267232
$717$	7.05702	0.263549
$718$	−2.72316	−0.101627
$719$	−20.4898	−0.764142	−0.382071	−	0.924133i	$-0.624789\pi$
$719$	−20.4898	−0.764142	−0.382071	+	0.924133i	$0.624789\pi$
$720$	2.78773	0.103893
$721$	5.61145	0.208981
$722$	−7.38269	−0.274755
$723$	−66.2667	−2.46449
$724$	−12.8211	−0.476492
$725$	−11.4110	−0.423795
$726$	25.7129	0.954296
$727$	−12.1877	−0.452017	−0.226008	−	0.974125i	$-0.572568\pi$
$727$	−12.1877	−0.452017	−0.226008	+	0.974125i	$0.572568\pi$
$728$	6.21936	0.230505
$729$	−26.1565	−0.968758
$730$	−0.512135	−0.0189550
$731$	−18.0499	−0.667598
$732$	25.2952	0.934939
$733$	18.9243	0.698986	0.349493	−	0.936939i	$-0.386354\pi$
$733$	18.9243	0.698986	0.349493	+	0.936939i	$0.386354\pi$
$734$	17.2015	0.634918
$735$	2.30304	0.0849488
$736$	1.80201	0.0664231
$737$	1.75121	0.0645067
$738$	−10.1824	−0.374820
$739$	21.8538	0.803904	0.401952	−	0.915661i	$-0.368332\pi$
$739$	21.8538	0.803904	0.401952	+	0.915661i	$0.368332\pi$
$740$	−5.53247	−0.203378
$741$	77.9456	2.86340
$742$	−1.94856	−0.0715340
$743$	−22.5331	−0.826659	−0.413329	−	0.910582i	$-0.635634\pi$
$743$	−22.5331	−0.826659	−0.413329	+	0.910582i	$0.635634\pi$
$744$	−5.08571	−0.186451
$745$	8.42699	0.308741
$746$	13.9913	0.512260
$747$	13.3293	0.487694
$748$	3.85094	0.140804
$749$	−10.2691	−0.375226
$750$	20.9786	0.766030
$751$	−24.3609	−0.888943	−0.444471	−	0.895793i	$-0.646608\pi$
$751$	−24.3609	−0.888943	−0.444471	+	0.895793i	$0.646608\pi$
$752$	6.61137	0.241092
$753$	−7.33820	−0.267419
$754$	−17.2713	−0.628983
$755$	13.4670	0.490116
$756$	0.113478	0.00412716
$757$	52.9912	1.92600	0.963000	−	0.269502i	$-0.0868592\pi$
$757$	52.9912	1.92600	0.963000	+	0.269502i	$0.0868592\pi$
$758$	−10.0002	−0.363222
$759$	−2.98802	−0.108458
$760$	−4.84813	−0.175860
$761$	30.2224	1.09556	0.547781	−	0.836622i	$-0.315473\pi$
$761$	30.2224	1.09556	0.547781	+	0.836622i	$0.315473\pi$
$762$	35.1612	1.27376
$763$	−2.83932	−0.102790
$764$	18.0129	0.651683
$765$	15.7971	0.571146
$766$	−27.0124	−0.975996
$767$	−38.4355	−1.38782
$768$	2.43998	0.0880451
$769$	−49.3563	−1.77983	−0.889917	−	0.456122i	$-0.849238\pi$
$769$	−49.3563	−1.77983	−0.889917	+	0.456122i	$0.849238\pi$
$770$	0.641437	0.0231158
$771$	−47.8746	−1.72416
$772$	15.1617	0.545680
$773$	38.7733	1.39458	0.697289	−	0.716790i	$-0.254389\pi$
$773$	38.7733	1.39458	0.697289	+	0.716790i	$0.254389\pi$
$774$	9.40768	0.338152
$775$	−8.56471	−0.307653
$776$	5.15688	0.185121
$777$	14.3018	0.513073
$778$	−20.8651	−0.748050
$779$	17.7082	0.634462
$780$	14.3234	0.512861
$781$	−1.41319	−0.0505679
$782$	10.2114	0.365159
$783$	−0.315131	−0.0112619
$784$	1.00000	0.0357143
$785$	−11.7674	−0.419995
$786$	−30.9282	−1.10317
$787$	−37.4111	−1.33356	−0.666781	−	0.745254i	$-0.732328\pi$
$787$	−37.4111	−1.33356	−0.666781	+	0.745254i	$0.732328\pi$
$788$	−21.4802	−0.765202
$789$	−14.9585	−0.532537
$790$	1.10783	0.0394148
$791$	−12.4677	−0.443301
$792$	−2.00713	−0.0713201
$793$	64.4761	2.28961
$794$	−16.7013	−0.592706
$795$	−4.48761	−0.159159
$796$	10.9980	0.389813
$797$	10.6612	0.377638	0.188819	−	0.982012i	$-0.439534\pi$
$797$	10.6612	0.377638	0.188819	+	0.982012i	$0.439534\pi$
$798$	12.5327	0.443654
$799$	37.4644	1.32539
$800$	4.10910	0.145279
$801$	−55.3282	−1.95493
$802$	5.35935	0.189245
$803$	0.368730	0.0130122
$804$	6.28761	0.221747
$805$	1.70088	0.0599481
$806$	−12.9632	−0.456609
$807$	−5.87371	−0.206764
$808$	5.61400	0.197500
$809$	−22.0550	−0.775412	−0.387706	−	0.921783i	$-0.626732\pi$
$809$	−22.0550	−0.775412	−0.387706	+	0.921783i	$0.626732\pi$
$810$	8.62454	0.303035
$811$	−26.2601	−0.922117	−0.461058	−	0.887370i	$-0.652530\pi$
$811$	−26.2601	−0.922117	−0.461058	+	0.887370i	$0.652530\pi$
$812$	−2.77702	−0.0974542
$813$	48.1269	1.68788
$814$	3.98330	0.139615
$815$	−4.11222	−0.144045
$816$	13.8265	0.484025
$817$	−16.3609	−0.572394
$818$	−32.2009	−1.12588
$819$	−18.3688	−0.641859
$820$	3.25409	0.113638
$821$	−45.7374	−1.59625	−0.798124	−	0.602494i	$-0.794174\pi$
$821$	−45.7374	−1.59625	−0.798124	+	0.602494i	$0.794174\pi$
$822$	−12.3600	−0.431104
$823$	−2.78438	−0.0970575	−0.0485287	−	0.998822i	$-0.515453\pi$
$823$	−2.78438	−0.0970575	−0.0485287	+	0.998822i	$0.515453\pi$
$824$	5.61145	0.195484
$825$	−6.81352	−0.237216
$826$	−6.17997	−0.215029
$827$	−26.2614	−0.913200	−0.456600	−	0.889672i	$-0.650933\pi$
$827$	−26.2614	−0.913200	−0.456600	+	0.889672i	$0.650933\pi$
$828$	−5.32224	−0.184961
$829$	−18.1942	−0.631912	−0.315956	−	0.948774i	$-0.602325\pi$
$829$	−18.1942	−0.631912	−0.315956	+	0.948774i	$0.602325\pi$
$830$	−4.25978	−0.147859
$831$	12.8248	0.444889
$832$	6.21936	0.215618
$833$	5.66666	0.196338
$834$	4.34544	0.150470
$835$	−7.56333	−0.261740
$836$	3.49059	0.120724
$837$	−0.236526	−0.00817553
$838$	17.7818	0.614262
$839$	−0.254788	−0.00879625	−0.00439812	−	0.999990i	$-0.501400\pi$
$839$	−0.254788	−0.00879625	−0.00439812	+	0.999990i	$0.501400\pi$
$840$	2.30304	0.0794623
$841$	−21.2882	−0.734075
$842$	4.94597	0.170449
$843$	66.5491	2.29207
$844$	8.39451	0.288951
$845$	24.2392	0.833854
$846$	−19.5266	−0.671339
$847$	10.5382	0.362096
$848$	−1.94856	−0.0669140
$849$	50.7113	1.74041
$850$	23.2849	0.798664
$851$	10.5624	0.362074
$852$	−5.07396	−0.173831
$853$	−25.9294	−0.887807	−0.443904	−	0.896075i	$-0.646407\pi$
$853$	−25.9294	−0.887807	−0.443904	+	0.896075i	$0.646407\pi$
$854$	10.3670	0.354751
$855$	14.3189	0.489697
$856$	−10.2691	−0.350992
$857$	−46.0067	−1.57156	−0.785780	−	0.618506i	$-0.787738\pi$
$857$	−46.0067	−1.57156	−0.785780	+	0.618506i	$0.787738\pi$
$858$	−10.3127	−0.352068
$859$	−35.1956	−1.20086	−0.600429	−	0.799678i	$-0.705003\pi$
$859$	−35.1956	−1.20086	−0.600429	+	0.799678i	$0.705003\pi$
$860$	−3.00650	−0.102521
$861$	−8.41203	−0.286681
$862$	−1.00000	−0.0340601
$863$	29.9730	1.02029	0.510146	−	0.860088i	$-0.329591\pi$
$863$	29.9730	1.02029	0.510146	+	0.860088i	$0.329591\pi$
$864$	0.113478	0.00386061
$865$	9.22947	0.313811
$866$	15.4958	0.526569
$867$	36.8706	1.25219
$868$	−2.08433	−0.0707467
$869$	−0.797620	−0.0270574
$870$	−6.39558	−0.216830
$871$	16.0267	0.543046
$872$	−2.83932	−0.0961517
$873$	−15.2308	−0.515485
$874$	9.25588	0.313085
$875$	8.59786	0.290661
$876$	1.32390	0.0447304
$877$	−7.38703	−0.249442	−0.124721	−	0.992192i	$-0.539804\pi$
$877$	−7.38703	−0.249442	−0.124721	+	0.992192i	$0.539804\pi$
$878$	6.45344	0.217793
$879$	−37.1719	−1.25378
$880$	0.641437	0.0216228
$881$	−22.4275	−0.755601	−0.377800	−	0.925887i	$-0.623319\pi$
$881$	−22.4275	−0.755601	−0.377800	+	0.925887i	$0.623319\pi$
$882$	−2.95349	−0.0994493
$883$	20.7953	0.699817	0.349908	−	0.936784i	$-0.386213\pi$
$883$	20.7953	0.699817	0.349908	+	0.936784i	$0.386213\pi$
$884$	35.2430	1.18535
$885$	−14.2327	−0.478427
$886$	−11.5683	−0.388643
$887$	29.7581	0.999179	0.499589	−	0.866262i	$-0.333484\pi$
$887$	29.7581	0.999179	0.499589	+	0.866262i	$0.333484\pi$
$888$	14.3018	0.479936
$889$	14.4105	0.483311
$890$	17.6818	0.592695
$891$	−6.20954	−0.208028
$892$	14.9872	0.501810
$893$	33.9587	1.13638
$894$	−21.7843	−0.728576
$895$	6.74932	0.225605
$896$	1.00000	0.0334077
$897$	−27.3458	−0.913049
$898$	−1.04394	−0.0348369
$899$	5.78822	0.193048
$900$	−12.1362	−0.404540
$901$	−11.0419	−0.367857
$902$	−2.34290	−0.0780101
$903$	7.77200	0.258636
$904$	−12.4677	−0.414671
$905$	−12.1015	−0.402268
$906$	−34.8131	−1.15659
$907$	15.0954	0.501235	0.250617	−	0.968086i	$-0.419366\pi$
$907$	15.0954	0.501235	0.250617	+	0.968086i	$0.419366\pi$
$908$	12.4708	0.413859
$909$	−16.5809	−0.549954
$910$	5.87031	0.194599
$911$	43.7848	1.45065	0.725327	−	0.688404i	$-0.241688\pi$
$911$	43.7848	1.45065	0.725327	+	0.688404i	$0.241688\pi$
$912$	12.5327	0.415000
$913$	3.06698	0.101502
$914$	25.9981	0.859940
$915$	23.8756	0.789303
$916$	−6.92575	−0.228833
$917$	−12.6756	−0.418585
$918$	0.643043	0.0212236
$919$	−29.4151	−0.970314	−0.485157	−	0.874427i	$-0.661237\pi$
$919$	−29.4151	−0.970314	−0.485157	+	0.874427i	$0.661237\pi$
$920$	1.70088	0.0560763
$921$	−35.3879	−1.16607
$922$	26.0485	0.857863
$923$	−12.9332	−0.425702
$924$	−1.65815	−0.0545493
$925$	24.0852	0.791917
$926$	9.47750	0.311450
$927$	−16.5734	−0.544341
$928$	−2.77702	−0.0911601
$929$	−0.754014	−0.0247384	−0.0123692	−	0.999923i	$-0.503937\pi$
$929$	−0.754014	−0.0247384	−0.0123692	+	0.999923i	$0.503937\pi$
$930$	−4.80028	−0.157408
$931$	5.13641	0.168339
$932$	−12.4395	−0.407470
$933$	74.9663	2.45429
$934$	−0.719422	−0.0235402
$935$	3.63481	0.118871
$936$	−18.3688	−0.600404
$937$	43.1821	1.41070	0.705350	−	0.708860i	$-0.250790\pi$
$937$	43.1821	1.41070	0.705350	+	0.708860i	$0.250790\pi$
$938$	2.57691	0.0841392
$939$	15.2166	0.496576
$940$	6.24031	0.203537
$941$	−8.00678	−0.261014	−0.130507	−	0.991447i	$-0.541660\pi$
$941$	−8.00678	−0.261014	−0.130507	+	0.991447i	$0.541660\pi$
$942$	30.4194	0.991117
$943$	−6.21260	−0.202310
$944$	−6.17997	−0.201141
$945$	0.107109	0.00348427
$946$	2.16464	0.0703785
$947$	16.8238	0.546699	0.273350	−	0.961915i	$-0.411868\pi$
$947$	16.8238	0.546699	0.273350	+	0.961915i	$0.411868\pi$
$948$	−2.86380	−0.0930120
$949$	3.37454	0.109542
$950$	21.1060	0.684769
$951$	52.9509	1.71705
$952$	5.66666	0.183658
$953$	39.8102	1.28958	0.644790	−	0.764360i	$-0.276945\pi$
$953$	39.8102	1.28958	0.644790	+	0.764360i	$0.276945\pi$
$954$	5.75507	0.186327
$955$	17.0019	0.550170
$956$	2.89225	0.0935420
$957$	4.60472	0.148850
$958$	−24.5385	−0.792803
$959$	−5.06561	−0.163577
$960$	2.30304	0.0743302
$961$	−26.6556	−0.859857
$962$	36.4544	1.17534
$963$	30.3298	0.977364
$964$	−27.1587	−0.874724
$965$	14.3107	0.460679
$966$	−4.39688	−0.141467
$967$	−22.0758	−0.709908	−0.354954	−	0.934884i	$-0.615504\pi$
$967$	−22.0758	−0.709908	−0.354954	+	0.934884i	$0.615504\pi$
$968$	10.5382	0.338710
$969$	71.0187	2.28145
$970$	4.86746	0.156285
$971$	3.33084	0.106892	0.0534459	−	0.998571i	$-0.482980\pi$
$971$	3.33084	0.106892	0.0534459	+	0.998571i	$0.482980\pi$
$972$	−21.9545	−0.704192
$973$	1.78094	0.0570942
$974$	−17.5916	−0.563670
$975$	−62.3560	−1.99699
$976$	10.3670	0.331840
$977$	−6.93947	−0.222013	−0.111007	−	0.993820i	$-0.535407\pi$
$977$	−6.93947	−0.222013	−0.111007	+	0.993820i	$0.535407\pi$
$978$	10.6303	0.339921
$979$	−12.7306	−0.406873
$980$	0.943876	0.0301510
$981$	8.38592	0.267742
$982$	15.0733	0.481009
$983$	−24.3772	−0.777513	−0.388757	−	0.921340i	$-0.627095\pi$
$983$	−24.3772	−0.777513	−0.388757	+	0.921340i	$0.627095\pi$
$984$	−8.41203	−0.268166
$985$	−20.2747	−0.646006
$986$	−15.7364	−0.501150
$987$	−16.1316	−0.513474
$988$	31.9452	1.01631
$989$	5.73991	0.182518
$990$	−1.89448	−0.0602105
$991$	−1.29103	−0.0410108	−0.0205054	−	0.999790i	$-0.506528\pi$
$991$	−1.29103	−0.0410108	−0.0205054	+	0.999790i	$0.506528\pi$
$992$	−2.08433	−0.0661775
$993$	−53.8751	−1.70968
$994$	−2.07951	−0.0659581
$995$	10.3807	0.329091
$996$	11.0118	0.348922
$997$	−18.2892	−0.579225	−0.289613	−	0.957144i	$-0.593526\pi$
$997$	−18.2892	−0.579225	−0.289613	+	0.957144i	$0.593526\pi$
$998$	1.97964	0.0626645
$999$	0.665145	0.0210443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.21	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.21	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.43998 q^{3} +1.00000 q^{4} +0.943876 q^{5} -2.43998 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.95349 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.43998 q^{3} +1.00000 q^{4} +0.943876 q^{5} -2.43998 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.95349 q^{9} -0.943876 q^{10} +0.679577 q^{11} +2.43998 q^{12} +6.21936 q^{13} +1.00000 q^{14} +2.30304 q^{15} +1.00000 q^{16} +5.66666 q^{17} -2.95349 q^{18} +5.13641 q^{19} +0.943876 q^{20} -2.43998 q^{21} -0.679577 q^{22} -1.80201 q^{23} -2.43998 q^{24} -4.10910 q^{25} -6.21936 q^{26} -0.113478 q^{27} -1.00000 q^{28} +2.77702 q^{29} -2.30304 q^{30} +2.08433 q^{31} -1.00000 q^{32} +1.65815 q^{33} -5.66666 q^{34} -0.943876 q^{35} +2.95349 q^{36} -5.86143 q^{37} -5.13641 q^{38} +15.1751 q^{39} -0.943876 q^{40} +3.44758 q^{41} +2.43998 q^{42} -3.18527 q^{43} +0.679577 q^{44} +2.78773 q^{45} +1.80201 q^{46} +6.61137 q^{47} +2.43998 q^{48} +1.00000 q^{49} +4.10910 q^{50} +13.8265 q^{51} +6.21936 q^{52} -1.94856 q^{53} +0.113478 q^{54} +0.641437 q^{55} +1.00000 q^{56} +12.5327 q^{57} -2.77702 q^{58} -6.17997 q^{59} +2.30304 q^{60} +10.3670 q^{61} -2.08433 q^{62} -2.95349 q^{63} +1.00000 q^{64} +5.87031 q^{65} -1.65815 q^{66} +2.57691 q^{67} +5.66666 q^{68} -4.39688 q^{69} +0.943876 q^{70} -2.07951 q^{71} -2.95349 q^{72} +0.542587 q^{73} +5.86143 q^{74} -10.0261 q^{75} +5.13641 q^{76} -0.679577 q^{77} -15.1751 q^{78} -1.17370 q^{79} +0.943876 q^{80} -9.13736 q^{81} -3.44758 q^{82} +4.51307 q^{83} -2.43998 q^{84} +5.34863 q^{85} +3.18527 q^{86} +6.77586 q^{87} -0.679577 q^{88} -18.7332 q^{89} -2.78773 q^{90} -6.21936 q^{91} -1.80201 q^{92} +5.08571 q^{93} -6.61137 q^{94} +4.84813 q^{95} -2.43998 q^{96} -5.15688 q^{97} -1.00000 q^{98} +2.00713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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