LMFDB - Embedded newform 6031.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58083 q^{2} +0.172052 q^{3} +4.66069 q^{4} +0.569694 q^{5} -0.444038 q^{6} +4.52515 q^{7} -6.86679 q^{8} -2.97040 q^{9} +O(q^{10})$	\(q-2.58083 q^{2} +0.172052 q^{3} +4.66069 q^{4} +0.569694 q^{5} -0.444038 q^{6} +4.52515 q^{7} -6.86679 q^{8} -2.97040 q^{9} -1.47028 q^{10} +1.07769 q^{11} +0.801883 q^{12} -0.957891 q^{13} -11.6786 q^{14} +0.0980173 q^{15} +8.40065 q^{16} +3.97877 q^{17} +7.66610 q^{18} -6.15621 q^{19} +2.65517 q^{20} +0.778563 q^{21} -2.78133 q^{22} -5.58702 q^{23} -1.18145 q^{24} -4.67545 q^{25} +2.47215 q^{26} -1.02722 q^{27} +21.0903 q^{28} +0.0841341 q^{29} -0.252966 q^{30} +2.46160 q^{31} -7.94707 q^{32} +0.185419 q^{33} -10.2685 q^{34} +2.57795 q^{35} -13.8441 q^{36} +1.00000 q^{37} +15.8881 q^{38} -0.164807 q^{39} -3.91197 q^{40} +1.92106 q^{41} -2.00934 q^{42} +9.15470 q^{43} +5.02276 q^{44} -1.69222 q^{45} +14.4192 q^{46} -6.94877 q^{47} +1.44535 q^{48} +13.4770 q^{49} +12.0665 q^{50} +0.684556 q^{51} -4.46443 q^{52} -11.1070 q^{53} +2.65109 q^{54} +0.613952 q^{55} -31.0732 q^{56} -1.05919 q^{57} -0.217136 q^{58} -6.86528 q^{59} +0.456828 q^{60} +2.93144 q^{61} -6.35297 q^{62} -13.4415 q^{63} +3.70876 q^{64} -0.545705 q^{65} -0.478534 q^{66} -7.47767 q^{67} +18.5438 q^{68} -0.961260 q^{69} -6.65325 q^{70} +8.67426 q^{71} +20.3971 q^{72} -6.84894 q^{73} -2.58083 q^{74} -0.804423 q^{75} -28.6922 q^{76} +4.87669 q^{77} +0.425340 q^{78} +15.5952 q^{79} +4.78580 q^{80} +8.73446 q^{81} -4.95792 q^{82} -0.225770 q^{83} +3.62864 q^{84} +2.26668 q^{85} -23.6267 q^{86} +0.0144755 q^{87} -7.40025 q^{88} -8.92345 q^{89} +4.36733 q^{90} -4.33460 q^{91} -26.0394 q^{92} +0.423524 q^{93} +17.9336 q^{94} -3.50716 q^{95} -1.36731 q^{96} +10.8388 q^{97} -34.7818 q^{98} -3.20116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.58083	−1.82492	−0.912462	−	0.409162i	$-0.865821\pi$
$2$	−2.58083	−1.82492	−0.912462	+	0.409162i	$0.865821\pi$
$3$	0.172052	0.0993345	0.0496673	−	0.998766i	$-0.484184\pi$
$3$	0.172052	0.0993345	0.0496673	+	0.998766i	$0.484184\pi$
$4$	4.66069	2.33034
$5$	0.569694	0.254775	0.127387	−	0.991853i	$-0.459341\pi$
$5$	0.569694	0.254775	0.127387	+	0.991853i	$0.459341\pi$
$6$	−0.444038	−0.181278
$7$	4.52515	1.71034	0.855172	−	0.518344i	$-0.173451\pi$
$7$	4.52515	1.71034	0.855172	+	0.518344i	$0.173451\pi$
$8$	−6.86679	−2.42778
$9$	−2.97040	−0.990133
$10$	−1.47028	−0.464945
$11$	1.07769	0.324935	0.162467	−	0.986714i	$-0.448055\pi$
$11$	1.07769	0.324935	0.162467	+	0.986714i	$0.448055\pi$
$12$	0.801883	0.231484
$13$	−0.957891	−0.265671	−0.132836	−	0.991138i	$-0.542408\pi$
$13$	−0.957891	−0.265671	−0.132836	+	0.991138i	$0.542408\pi$
$14$	−11.6786	−3.12125
$15$	0.0980173	0.0253080
$16$	8.40065	2.10016
$17$	3.97877	0.964992	0.482496	−	0.875898i	$-0.339730\pi$
$17$	3.97877	0.964992	0.482496	+	0.875898i	$0.339730\pi$
$18$	7.66610	1.80692
$19$	−6.15621	−1.41233	−0.706166	−	0.708046i	$-0.749577\pi$
$19$	−6.15621	−1.41233	−0.706166	+	0.708046i	$0.749577\pi$
$20$	2.65517	0.593714
$21$	0.778563	0.169896
$22$	−2.78133	−0.592981
$23$	−5.58702	−1.16497	−0.582487	−	0.812840i	$-0.697920\pi$
$23$	−5.58702	−1.16497	−0.582487	+	0.812840i	$0.697920\pi$
$24$	−1.18145	−0.241162
$25$	−4.67545	−0.935090
$26$	2.47215	0.484829
$27$	−1.02722	−0.197689
$28$	21.0903	3.98569
$29$	0.0841341	0.0156233	0.00781165	−	0.999969i	$-0.497513\pi$
$29$	0.0841341	0.0156233	0.00781165	+	0.999969i	$0.497513\pi$
$30$	−0.252966	−0.0461851
$31$	2.46160	0.442116	0.221058	−	0.975261i	$-0.429049\pi$
$31$	2.46160	0.442116	0.221058	+	0.975261i	$0.429049\pi$
$32$	−7.94707	−1.40486
$33$	0.185419	0.0322772
$34$	−10.2685	−1.76104
$35$	2.57795	0.435753
$36$	−13.8441	−2.30735
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	15.8881	2.57740
$39$	−0.164807	−0.0263903
$40$	−3.91197	−0.618537
$41$	1.92106	0.300019	0.150009	−	0.988685i	$-0.452070\pi$
$41$	1.92106	0.300019	0.150009	+	0.988685i	$0.452070\pi$
$42$	−2.00934	−0.310048
$43$	9.15470	1.39608	0.698039	−	0.716059i	$-0.254056\pi$
$43$	9.15470	1.39608	0.698039	+	0.716059i	$0.254056\pi$
$44$	5.02276	0.757210
$45$	−1.69222	−0.252261
$46$	14.4192	2.12599
$47$	−6.94877	−1.01358	−0.506791	−	0.862069i	$-0.669168\pi$
$47$	−6.94877	−1.01358	−0.506791	+	0.862069i	$0.669168\pi$
$48$	1.44535	0.208619
$49$	13.4770	1.92528
$50$	12.0665	1.70647
$51$	0.684556	0.0958571
$52$	−4.46443	−0.619105
$53$	−11.1070	−1.52567	−0.762833	−	0.646596i	$-0.776192\pi$
$53$	−11.1070	−1.52567	−0.762833	+	0.646596i	$0.776192\pi$
$54$	2.65109	0.360767
$55$	0.613952	0.0827852
$56$	−31.0732	−4.15234
$57$	−1.05919	−0.140293
$58$	−0.217136	−0.0285113
$59$	−6.86528	−0.893783	−0.446891	−	0.894588i	$-0.647469\pi$
$59$	−6.86528	−0.893783	−0.446891	+	0.894588i	$0.647469\pi$
$60$	0.456828	0.0589763
$61$	2.93144	0.375332	0.187666	−	0.982233i	$-0.439908\pi$
$61$	2.93144	0.375332	0.187666	+	0.982233i	$0.439908\pi$
$62$	−6.35297	−0.806828
$63$	−13.4415	−1.69347
$64$	3.70876	0.463595
$65$	−0.545705	−0.0676863
$66$	−0.478534	−0.0589035
$67$	−7.47767	−0.913543	−0.456771	−	0.889584i	$-0.650994\pi$
$67$	−7.47767	−0.913543	−0.456771	+	0.889584i	$0.650994\pi$
$68$	18.5438	2.24876
$69$	−0.961260	−0.115722
$70$	−6.65325	−0.795216
$71$	8.67426	1.02944	0.514722	−	0.857357i	$-0.327895\pi$
$71$	8.67426	1.02944	0.514722	+	0.857357i	$0.327895\pi$
$72$	20.3971	2.40382
$73$	−6.84894	−0.801608	−0.400804	−	0.916164i	$-0.631269\pi$
$73$	−6.84894	−0.801608	−0.400804	+	0.916164i	$0.631269\pi$
$74$	−2.58083	−0.300016
$75$	−0.804423	−0.0928867
$76$	−28.6922	−3.29122
$77$	4.87669	0.555751
$78$	0.425340	0.0481603
$79$	15.5952	1.75460	0.877298	−	0.479946i	$-0.159344\pi$
$79$	15.5952	1.75460	0.877298	+	0.479946i	$0.159344\pi$
$80$	4.78580	0.535069
$81$	8.73446	0.970495
$82$	−4.95792	−0.547511
$83$	−0.225770	−0.0247814	−0.0123907	−	0.999923i	$-0.503944\pi$
$83$	−0.225770	−0.0247814	−0.0123907	+	0.999923i	$0.503944\pi$
$84$	3.62864	0.395917
$85$	2.26668	0.245856
$86$	−23.6267	−2.54774
$87$	0.0144755	0.00155193
$88$	−7.40025	−0.788869
$89$	−8.92345	−0.945884	−0.472942	−	0.881094i	$-0.656808\pi$
$89$	−8.92345	−0.945884	−0.472942	+	0.881094i	$0.656808\pi$
$90$	4.36733	0.460357
$91$	−4.33460	−0.454389
$92$	−26.0394	−2.71479
$93$	0.423524	0.0439174
$94$	17.9336	1.84971
$95$	−3.50716	−0.359827
$96$	−1.36731	−0.139551
$97$	10.8388	1.10051	0.550255	−	0.834996i	$-0.314530\pi$
$97$	10.8388	1.10051	0.550255	+	0.834996i	$0.314530\pi$
$98$	−34.7818	−3.51349
$99$	−3.20116	−0.321729
$100$	−21.7908	−2.17908
$101$	−16.3897	−1.63084	−0.815418	−	0.578872i	$-0.803493\pi$
$101$	−16.3897	−1.63084	−0.815418	+	0.578872i	$0.803493\pi$
$102$	−1.76672	−0.174932
$103$	5.30225	0.522446	0.261223	−	0.965278i	$-0.415874\pi$
$103$	5.30225	0.522446	0.261223	+	0.965278i	$0.415874\pi$
$104$	6.57763	0.644990
$105$	0.443543	0.0432853
$106$	28.6653	2.78422
$107$	−3.23891	−0.313117	−0.156558	−	0.987669i	$-0.550040\pi$
$107$	−3.23891	−0.313117	−0.156558	+	0.987669i	$0.550040\pi$
$108$	−4.78756	−0.460683
$109$	2.84581	0.272579	0.136289	−	0.990669i	$-0.456482\pi$
$109$	2.84581	0.272579	0.136289	+	0.990669i	$0.456482\pi$
$110$	−1.58451	−0.151077
$111$	0.172052	0.0163305
$112$	38.0142	3.59200
$113$	−4.94892	−0.465555	−0.232778	−	0.972530i	$-0.574781\pi$
$113$	−4.94892	−0.465555	−0.232778	+	0.972530i	$0.574781\pi$
$114$	2.73359	0.256025
$115$	−3.18289	−0.296806
$116$	0.392123	0.0364077
$117$	2.84532	0.263050
$118$	17.7181	1.63108
$119$	18.0045	1.65047
$120$	−0.673064	−0.0614421
$121$	−9.83859	−0.894417
$122$	−7.56555	−0.684952
$123$	0.330522	0.0298022
$124$	11.4727	1.03028
$125$	−5.51205	−0.493012
$126$	34.6902	3.09045
$127$	−19.3185	−1.71424	−0.857118	−	0.515119i	$-0.827748\pi$
$127$	−19.3185	−1.71424	−0.857118	+	0.515119i	$0.827748\pi$
$128$	6.32247	0.558832
$129$	1.57509	0.138679
$130$	1.40837	0.123522
$131$	−11.9504	−1.04411	−0.522055	−	0.852912i	$-0.674834\pi$
$131$	−11.9504	−1.04411	−0.522055	+	0.852912i	$0.674834\pi$
$132$	0.864179	0.0752171
$133$	−27.8578	−2.41557
$134$	19.2986	1.66715
$135$	−0.585202	−0.0503662
$136$	−27.3213	−2.34279
$137$	−16.7638	−1.43223	−0.716113	−	0.697984i	$-0.754081\pi$
$137$	−16.7638	−1.43223	−0.716113	+	0.697984i	$0.754081\pi$
$138$	2.48085	0.211184
$139$	4.16021	0.352864	0.176432	−	0.984313i	$-0.443544\pi$
$139$	4.16021	0.352864	0.176432	+	0.984313i	$0.443544\pi$
$140$	12.0150	1.01545
$141$	−1.19555	−0.100684
$142$	−22.3868	−1.87866
$143$	−1.03231	−0.0863258
$144$	−24.9533	−2.07944
$145$	0.0479307	0.00398043
$146$	17.6760	1.46287
$147$	2.31874	0.191247
$148$	4.66069	0.383106
$149$	10.4117	0.852963	0.426482	−	0.904496i	$-0.359753\pi$
$149$	10.4117	0.852963	0.426482	+	0.904496i	$0.359753\pi$
$150$	2.07608	0.169511
$151$	−17.9145	−1.45787	−0.728933	−	0.684585i	$-0.759983\pi$
$151$	−17.9145	−1.45787	−0.728933	+	0.684585i	$0.759983\pi$
$152$	42.2734	3.42883
$153$	−11.8185	−0.955470
$154$	−12.5859	−1.01420
$155$	1.40236	0.112640
$156$	−0.768116	−0.0614985
$157$	−9.41079	−0.751063	−0.375532	−	0.926810i	$-0.622540\pi$
$157$	−9.41079	−0.751063	−0.375532	+	0.926810i	$0.622540\pi$
$158$	−40.2486	−3.20200
$159$	−1.91099	−0.151551
$160$	−4.52740	−0.357922
$161$	−25.2821	−1.99251
$162$	−22.5422	−1.77108
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	8.95345	0.699147
$165$	0.105632	0.00822343
$166$	0.582674	0.0452242
$167$	3.42238	0.264832	0.132416	−	0.991194i	$-0.457727\pi$
$167$	3.42238	0.264832	0.132416	+	0.991194i	$0.457727\pi$
$168$	−5.34623	−0.412470
$169$	−12.0824	−0.929419
$170$	−5.84992	−0.448668
$171$	18.2864	1.39840
$172$	42.6672	3.25334
$173$	−2.93919	−0.223463	−0.111731	−	0.993738i	$-0.535640\pi$
$173$	−2.93919	−0.223463	−0.111731	+	0.993738i	$0.535640\pi$
$174$	−0.0373588	−0.00283216
$175$	−21.1571	−1.59933
$176$	9.05327	0.682416
$177$	−1.18119	−0.0887835
$178$	23.0299	1.72617
$179$	2.43710	0.182157	0.0910786	−	0.995844i	$-0.470969\pi$
$179$	2.43710	0.182157	0.0910786	+	0.995844i	$0.470969\pi$
$180$	−7.88690	−0.587855
$181$	12.5987	0.936453	0.468227	−	0.883608i	$-0.344893\pi$
$181$	12.5987	0.936453	0.468227	+	0.883608i	$0.344893\pi$
$182$	11.1869	0.829225
$183$	0.504361	0.0372834
$184$	38.3649	2.82830
$185$	0.569694	0.0418847
$186$	−1.09304	−0.0801459
$187$	4.28786	0.313560
$188$	−32.3861	−2.36200
$189$	−4.64833	−0.338116
$190$	9.05138	0.656656
$191$	−25.4955	−1.84479	−0.922394	−	0.386251i	$-0.873770\pi$
$191$	−25.4955	−1.84479	−0.922394	+	0.386251i	$0.873770\pi$
$192$	0.638101	0.0460510
$193$	7.35286	0.529271	0.264635	−	0.964349i	$-0.414748\pi$
$193$	7.35286	0.529271	0.264635	+	0.964349i	$0.414748\pi$
$194$	−27.9730	−2.00835
$195$	−0.0938898	−0.00672359
$196$	62.8119	4.48657
$197$	−11.2423	−0.800978	−0.400489	−	0.916302i	$-0.631160\pi$
$197$	−11.2423	−0.800978	−0.400489	+	0.916302i	$0.631160\pi$
$198$	8.26165	0.587130
$199$	10.3221	0.731712	0.365856	−	0.930672i	$-0.380776\pi$
$199$	10.3221	0.731712	0.365856	+	0.930672i	$0.380776\pi$
$200$	32.1053	2.27019
$201$	−1.28655	−0.0907463
$202$	42.2991	2.97615
$203$	0.380719	0.0267212
$204$	3.19051	0.223380
$205$	1.09441	0.0764372
$206$	−13.6842	−0.953424
$207$	16.5957	1.15348
$208$	−8.04690	−0.557952
$209$	−6.63447	−0.458916
$210$	−1.14471	−0.0789924
$211$	−11.8281	−0.814279	−0.407140	−	0.913366i	$-0.633474\pi$
$211$	−11.8281	−0.814279	−0.407140	+	0.913366i	$0.633474\pi$
$212$	−51.7663	−3.55533
$213$	1.49243	0.102259
$214$	8.35907	0.571414
$215$	5.21538	0.355686
$216$	7.05372	0.479945
$217$	11.1391	0.756171
$218$	−7.34455	−0.497435
$219$	−1.17838	−0.0796273
$220$	2.86144	0.192918
$221$	−3.81122	−0.256371
$222$	−0.444038	−0.0298019
$223$	−20.6702	−1.38418	−0.692088	−	0.721813i	$-0.743309\pi$
$223$	−20.6702	−1.38418	−0.692088	+	0.721813i	$0.743309\pi$
$224$	−35.9617	−2.40279
$225$	13.8879	0.925863
$226$	12.7723	0.849603
$227$	4.80847	0.319150	0.159575	−	0.987186i	$-0.448988\pi$
$227$	4.80847	0.319150	0.159575	+	0.987186i	$0.448988\pi$
$228$	−4.93656	−0.326932
$229$	−1.23856	−0.0818461	−0.0409231	−	0.999162i	$-0.513030\pi$
$229$	−1.23856	−0.0818461	−0.0409231	+	0.999162i	$0.513030\pi$
$230$	8.21451	0.541648
$231$	0.839047	0.0552052
$232$	−0.577731	−0.0379299
$233$	−23.5382	−1.54204	−0.771019	−	0.636812i	$-0.780253\pi$
$233$	−23.5382	−1.54204	−0.771019	+	0.636812i	$0.780253\pi$
$234$	−7.34328	−0.480045
$235$	−3.95867	−0.258235
$236$	−31.9969	−2.08282
$237$	2.68319	0.174292
$238$	−46.4666	−3.01198
$239$	14.7810	0.956105	0.478052	−	0.878331i	$-0.341343\pi$
$239$	14.7810	0.956105	0.478052	+	0.878331i	$0.341343\pi$
$240$	0.823409	0.0531508
$241$	18.5744	1.19648	0.598241	−	0.801316i	$-0.295867\pi$
$241$	18.5744	1.19648	0.598241	+	0.801316i	$0.295867\pi$
$242$	25.3917	1.63224
$243$	4.58445	0.294093
$244$	13.6625	0.874653
$245$	7.67774	0.490513
$246$	−0.853023	−0.0543867
$247$	5.89698	0.375216
$248$	−16.9033	−1.07336
$249$	−0.0388442	−0.00246165
$250$	14.2257	0.899710
$251$	−13.0036	−0.820783	−0.410391	−	0.911909i	$-0.634608\pi$
$251$	−13.0036	−0.820783	−0.410391	+	0.911909i	$0.634608\pi$
$252$	−62.6466	−3.94637
$253$	−6.02106	−0.378541
$254$	49.8577	3.12835
$255$	0.389988	0.0244220
$256$	−23.7347	−1.48342
$257$	−14.6285	−0.912501	−0.456251	−	0.889851i	$-0.650808\pi$
$257$	−14.6285	−0.912501	−0.456251	+	0.889851i	$0.650808\pi$
$258$	−4.06504	−0.253078
$259$	4.52515	0.281179
$260$	−2.54336	−0.157732
$261$	−0.249912	−0.0154691
$262$	30.8419	1.90542
$263$	−13.2110	−0.814627	−0.407314	−	0.913288i	$-0.633534\pi$
$263$	−13.2110	−0.814627	−0.407314	+	0.913288i	$0.633534\pi$
$264$	−1.27323	−0.0783620
$265$	−6.32760	−0.388701
$266$	71.8962	4.40824
$267$	−1.53530	−0.0939590
$268$	−34.8511	−2.12887
$269$	21.3431	1.30131	0.650657	−	0.759372i	$-0.274494\pi$
$269$	21.3431	1.30131	0.650657	+	0.759372i	$0.274494\pi$
$270$	1.51031	0.0919144
$271$	−0.497820	−0.0302404	−0.0151202	−	0.999886i	$-0.504813\pi$
$271$	−0.497820	−0.0302404	−0.0151202	+	0.999886i	$0.504813\pi$
$272$	33.4242	2.02664
$273$	−0.745778	−0.0451365
$274$	43.2645	2.61370
$275$	−5.03867	−0.303843
$276$	−4.48014	−0.269672
$277$	29.6130	1.77927	0.889637	−	0.456668i	$-0.150957\pi$
$277$	29.6130	1.77927	0.889637	+	0.456668i	$0.150957\pi$
$278$	−10.7368	−0.643950
$279$	−7.31193	−0.437754
$280$	−17.7022	−1.05791
$281$	21.6440	1.29117	0.645587	−	0.763687i	$-0.276613\pi$
$281$	21.6440	1.29117	0.645587	+	0.763687i	$0.276613\pi$
$282$	3.08552	0.183740
$283$	25.7593	1.53123	0.765616	−	0.643297i	$-0.222434\pi$
$283$	25.7593	1.53123	0.765616	+	0.643297i	$0.222434\pi$
$284$	40.4280	2.39896
$285$	−0.603415	−0.0357432
$286$	2.66421	0.157538
$287$	8.69306	0.513135
$288$	23.6060	1.39100
$289$	−1.16942	−0.0687897
$290$	−0.123701	−0.00726397
$291$	1.86484	0.109319
$292$	−31.9208	−1.86802
$293$	26.1609	1.52834	0.764169	−	0.645016i	$-0.223149\pi$
$293$	26.1609	1.52834	0.764169	+	0.645016i	$0.223149\pi$
$294$	−5.98429	−0.349011
$295$	−3.91111	−0.227713
$296$	−6.86679	−0.399124
$297$	−1.10702	−0.0642360
$298$	−26.8709	−1.55659
$299$	5.35175	0.309500
$300$	−3.74916	−0.216458
$301$	41.4264	2.38778
$302$	46.2344	2.66049
$303$	−2.81989	−0.161998
$304$	−51.7162	−2.96613
$305$	1.67002	0.0956252
$306$	30.5016	1.74366
$307$	26.7997	1.52954	0.764770	−	0.644303i	$-0.222852\pi$
$307$	26.7997	1.52954	0.764770	+	0.644303i	$0.222852\pi$
$308$	22.7287	1.29509
$309$	0.912265	0.0518970
$310$	−3.61925	−0.205560
$311$	−27.8665	−1.58016	−0.790082	−	0.613001i	$-0.789962\pi$
$311$	−27.8665	−1.58016	−0.790082	+	0.613001i	$0.789962\pi$
$312$	1.13170	0.0640698
$313$	9.88673	0.558831	0.279416	−	0.960170i	$-0.409859\pi$
$313$	9.88673	0.558831	0.279416	+	0.960170i	$0.409859\pi$
$314$	24.2877	1.37063
$315$	−7.65754	−0.431453
$316$	72.6844	4.08881
$317$	−16.9734	−0.953322	−0.476661	−	0.879087i	$-0.658153\pi$
$317$	−16.9734	−0.953322	−0.476661	+	0.879087i	$0.658153\pi$
$318$	4.93194	0.276569
$319$	0.0906702	0.00507655
$320$	2.11286	0.118112
$321$	−0.557262	−0.0311033
$322$	65.2488	3.63617
$323$	−24.4941	−1.36289
$324$	40.7086	2.26159
$325$	4.47857	0.248426
$326$	−2.58083	−0.142939
$327$	0.489628	0.0270765
$328$	−13.1915	−0.728378
$329$	−31.4442	−1.73358
$330$	−0.272618	−0.0150071
$331$	−29.0167	−1.59490	−0.797451	−	0.603383i	$-0.793819\pi$
$331$	−29.0167	−1.59490	−0.797451	+	0.603383i	$0.793819\pi$
$332$	−1.05224	−0.0577493
$333$	−2.97040	−0.162777
$334$	−8.83258	−0.483297
$335$	−4.25998	−0.232748
$336$	6.54043	0.356810
$337$	21.0348	1.14584	0.572920	−	0.819611i	$-0.305811\pi$
$337$	21.0348	1.14584	0.572920	+	0.819611i	$0.305811\pi$
$338$	31.1828	1.69612
$339$	−0.851474	−0.0462457
$340$	10.5643	0.572929
$341$	2.65283	0.143659
$342$	−47.1941	−2.55197
$343$	29.3092	1.58255
$344$	−62.8634	−3.38937
$345$	−0.547624	−0.0294831
$346$	7.58556	0.407802
$347$	32.5405	1.74687	0.873433	−	0.486944i	$-0.161889\pi$
$347$	32.5405	1.74687	0.873433	+	0.486944i	$0.161889\pi$
$348$	0.0674657	0.00361654
$349$	2.97743	0.159378	0.0796891	−	0.996820i	$-0.474607\pi$
$349$	2.97743	0.159378	0.0796891	+	0.996820i	$0.474607\pi$
$350$	54.6029	2.91865
$351$	0.983966	0.0525202
$352$	−8.56446	−0.456487
$353$	−3.09117	−0.164527	−0.0822633	−	0.996611i	$-0.526215\pi$
$353$	−3.09117	−0.164527	−0.0822633	+	0.996611i	$0.526215\pi$
$354$	3.04845	0.162023
$355$	4.94167	0.262277
$356$	−41.5894	−2.20424
$357$	3.09772	0.163949
$358$	−6.28974	−0.332423
$359$	−5.49007	−0.289755	−0.144877	−	0.989450i	$-0.546279\pi$
$359$	−5.49007	−0.289755	−0.144877	+	0.989450i	$0.546279\pi$
$360$	11.6201	0.612433
$361$	18.8990	0.994682
$362$	−32.5151	−1.70896
$363$	−1.69275	−0.0888465
$364$	−20.2022	−1.05888
$365$	−3.90180	−0.204230
$366$	−1.30167	−0.0680394
$367$	5.36974	0.280298	0.140149	−	0.990130i	$-0.455242\pi$
$367$	5.36974	0.280298	0.140149	+	0.990130i	$0.455242\pi$
$368$	−46.9346	−2.44663
$369$	−5.70630	−0.297058
$370$	−1.47028	−0.0764364
$371$	−50.2609	−2.60941
$372$	1.97391	0.102343
$373$	26.7411	1.38460	0.692301	−	0.721609i	$-0.256597\pi$
$373$	26.7411	1.38460	0.692301	+	0.721609i	$0.256597\pi$
$374$	−11.0663	−0.572222
$375$	−0.948361	−0.0489732
$376$	47.7157	2.46075
$377$	−0.0805912	−0.00415066
$378$	11.9966	0.617036
$379$	−14.1740	−0.728067	−0.364034	−	0.931386i	$-0.618601\pi$
$379$	−14.1740	−0.728067	−0.364034	+	0.931386i	$0.618601\pi$
$380$	−16.3458	−0.838521
$381$	−3.32379	−0.170283
$382$	65.7995	3.36660
$383$	−34.3175	−1.75354	−0.876772	−	0.480907i	$-0.840308\pi$
$383$	−34.3175	−1.75354	−0.876772	+	0.480907i	$0.840308\pi$
$384$	1.08780	0.0555114
$385$	2.77822	0.141591
$386$	−18.9765	−0.965878
$387$	−27.1931	−1.38230
$388$	50.5162	2.56457
$389$	−14.2550	−0.722757	−0.361378	−	0.932419i	$-0.617694\pi$
$389$	−14.2550	−0.722757	−0.361378	+	0.932419i	$0.617694\pi$
$390$	0.242314	0.0122700
$391$	−22.2294	−1.12419
$392$	−92.5435	−4.67415
$393$	−2.05609	−0.103716
$394$	29.0144	1.46172
$395$	8.88449	0.447027
$396$	−14.9196	−0.749738
$397$	32.4642	1.62933	0.814665	−	0.579932i	$-0.196921\pi$
$397$	32.4642	1.62933	0.814665	+	0.579932i	$0.196921\pi$
$398$	−26.6395	−1.33532
$399$	−4.79300	−0.239950
$400$	−39.2768	−1.96384
$401$	−15.1797	−0.758036	−0.379018	−	0.925389i	$-0.623738\pi$
$401$	−15.1797	−0.758036	−0.379018	+	0.925389i	$0.623738\pi$
$402$	3.32037	0.165605
$403$	−2.35794	−0.117457
$404$	−76.3873	−3.80041
$405$	4.97597	0.247258
$406$	−0.982572	−0.0487642
$407$	1.07769	0.0534190
$408$	−4.70071	−0.232720
$409$	−35.1321	−1.73717	−0.868586	−	0.495539i	$-0.834971\pi$
$409$	−35.1321	−1.73717	−0.868586	+	0.495539i	$0.834971\pi$
$410$	−2.82450	−0.139492
$411$	−2.88425	−0.142270
$412$	24.7121	1.21748
$413$	−31.0664	−1.52868
$414$	−42.8306	−2.10501
$415$	−0.128620	−0.00631369
$416$	7.61243	0.373230
$417$	0.715774	0.0350516
$418$	17.1224	0.837486
$419$	15.2729	0.746132	0.373066	−	0.927805i	$-0.378307\pi$
$419$	15.2729	0.746132	0.373066	+	0.927805i	$0.378307\pi$
$420$	2.06721	0.100870
$421$	−22.9420	−1.11812	−0.559062	−	0.829126i	$-0.688839\pi$
$421$	−22.9420	−1.11812	−0.559062	+	0.829126i	$0.688839\pi$
$422$	30.5263	1.48600
$423$	20.6406	1.00358
$424$	76.2695	3.70398
$425$	−18.6025	−0.902354
$426$	−3.85170	−0.186616
$427$	13.2652	0.641947
$428$	−15.0955	−0.729670
$429$	−0.177611	−0.00857513
$430$	−13.4600	−0.649099
$431$	−1.06171	−0.0511406	−0.0255703	−	0.999673i	$-0.508140\pi$
$431$	−1.06171	−0.0511406	−0.0255703	+	0.999673i	$0.508140\pi$
$432$	−8.62933	−0.415179
$433$	−26.1501	−1.25669	−0.628347	−	0.777933i	$-0.716268\pi$
$433$	−26.1501	−1.25669	−0.628347	+	0.777933i	$0.716268\pi$
$434$	−28.7481	−1.37995
$435$	0.00824659	0.000395394 0
$436$	13.2634	0.635203
$437$	34.3949	1.64533
$438$	3.04119	0.145314
$439$	−13.7641	−0.656925	−0.328463	−	0.944517i	$-0.606531\pi$
$439$	−13.7641	−0.656925	−0.328463	+	0.944517i	$0.606531\pi$
$440$	−4.21588	−0.200984
$441$	−40.0319	−1.90628
$442$	9.83612	0.467857
$443$	−6.10563	−0.290087	−0.145044	−	0.989425i	$-0.546332\pi$
$443$	−6.10563	−0.290087	−0.145044	+	0.989425i	$0.546332\pi$
$444$	0.801883	0.0380557
$445$	−5.08364	−0.240988
$446$	53.3462	2.52601
$447$	1.79137	0.0847287
$448$	16.7827	0.792907
$449$	6.78543	0.320224	0.160112	−	0.987099i	$-0.448814\pi$
$449$	6.78543	0.320224	0.160112	+	0.987099i	$0.448814\pi$
$450$	−35.8424	−1.68963
$451$	2.07030	0.0974865
$452$	−23.0654	−1.08490
$453$	−3.08224	−0.144816
$454$	−12.4099	−0.582423
$455$	−2.46939	−0.115767
$456$	7.27325	0.340601
$457$	30.3925	1.42170	0.710850	−	0.703344i	$-0.248311\pi$
$457$	30.3925	1.42170	0.710850	+	0.703344i	$0.248311\pi$
$458$	3.19651	0.149363
$459$	−4.08707	−0.190768
$460$	−14.8345	−0.691661
$461$	−6.47965	−0.301787	−0.150894	−	0.988550i	$-0.548215\pi$
$461$	−6.47965	−0.301787	−0.150894	+	0.988550i	$0.548215\pi$
$462$	−2.16544	−0.100745
$463$	0.628385	0.0292035	0.0146018	−	0.999893i	$-0.495352\pi$
$463$	0.628385	0.0292035	0.0146018	+	0.999893i	$0.495352\pi$
$464$	0.706781	0.0328115
$465$	0.241279	0.0111891
$466$	60.7481	2.81410
$467$	−6.19505	−0.286673	−0.143336	−	0.989674i	$-0.545783\pi$
$467$	−6.19505	−0.286673	−0.143336	+	0.989674i	$0.545783\pi$
$468$	13.2611	0.612996
$469$	−33.8376	−1.56247
$470$	10.2167	0.471260
$471$	−1.61915	−0.0746065
$472$	47.1424	2.16991
$473$	9.86590	0.453635
$474$	−6.92486	−0.318070
$475$	28.7831	1.32066
$476$	83.9134	3.84616
$477$	32.9923	1.51061
$478$	−38.1473	−1.74482
$479$	−35.4051	−1.61770	−0.808851	−	0.588014i	$-0.799910\pi$
$479$	−35.4051	−1.61770	−0.808851	+	0.588014i	$0.799910\pi$
$480$	−0.778951	−0.0355541
$481$	−0.957891	−0.0436761
$482$	−47.9374	−2.18349
$483$	−4.34984	−0.197925
$484$	−45.8546	−2.08430
$485$	6.17479	0.280383
$486$	−11.8317	−0.536696
$487$	6.00125	0.271943	0.135971	−	0.990713i	$-0.456584\pi$
$487$	6.00125	0.271943	0.135971	+	0.990713i	$0.456584\pi$
$488$	−20.1296	−0.911223
$489$	0.172052	0.00778048
$490$	−19.8150	−0.895149
$491$	31.8372	1.43679	0.718396	−	0.695634i	$-0.244877\pi$
$491$	31.8372	1.43679	0.718396	+	0.695634i	$0.244877\pi$
$492$	1.54046	0.0694494
$493$	0.334750	0.0150764
$494$	−15.2191	−0.684740
$495$	−1.82368	−0.0819684
$496$	20.6790	0.928515
$497$	39.2523	1.76071
$498$	0.100250	0.00449233
$499$	8.65752	0.387564	0.193782	−	0.981045i	$-0.437925\pi$
$499$	8.65752	0.387564	0.193782	+	0.981045i	$0.437925\pi$
$500$	−25.6899	−1.14889
$501$	0.588829	0.0263069
$502$	33.5602	1.49787
$503$	24.0202	1.07101	0.535505	−	0.844532i	$-0.320121\pi$
$503$	24.0202	1.07101	0.535505	+	0.844532i	$0.320121\pi$
$504$	92.2999	4.11136
$505$	−9.33712	−0.415496
$506$	15.5393	0.690807
$507$	−2.07881	−0.0923234
$508$	−90.0374	−3.99476
$509$	7.40930	0.328411	0.164206	−	0.986426i	$-0.447494\pi$
$509$	7.40930	0.328411	0.164206	+	0.986426i	$0.447494\pi$
$510$	−1.00649	−0.0445682
$511$	−30.9925	−1.37103
$512$	48.6104	2.14830
$513$	6.32380	0.279202
$514$	37.7537	1.66524
$515$	3.02066	0.133106
$516$	7.34100	0.323170
$517$	−7.48860	−0.329348
$518$	−11.6786	−0.513130
$519$	−0.505695	−0.0221976
$520$	3.74724	0.164327
$521$	−34.6706	−1.51895	−0.759474	−	0.650537i	$-0.774544\pi$
$521$	−34.6706	−1.51895	−0.759474	+	0.650537i	$0.774544\pi$
$522$	0.644980	0.0282300
$523$	−30.9432	−1.35305	−0.676525	−	0.736419i	$-0.736515\pi$
$523$	−30.9432	−1.35305	−0.676525	+	0.736419i	$0.736515\pi$
$524$	−55.6970	−2.43314
$525$	−3.64013	−0.158868
$526$	34.0954	1.48663
$527$	9.79412	0.426639
$528$	1.55764	0.0677875
$529$	8.21477	0.357164
$530$	16.3305	0.709350
$531$	20.3926	0.884964
$532$	−129.836	−5.62912
$533$	−1.84016	−0.0797062
$534$	3.96236	0.171468
$535$	−1.84519	−0.0797743
$536$	51.3476	2.21788
$537$	0.419309	0.0180945
$538$	−55.0830	−2.37480
$539$	14.5239	0.625590
$540$	−2.72745	−0.117371
$541$	−20.6505	−0.887836	−0.443918	−	0.896067i	$-0.646412\pi$
$541$	−20.6505	−0.887836	−0.443918	+	0.896067i	$0.646412\pi$
$542$	1.28479	0.0551864
$543$	2.16764	0.0930221
$544$	−31.6195	−1.35568
$545$	1.62124	0.0694462
$546$	1.92473	0.0823707
$547$	−34.2089	−1.46267	−0.731334	−	0.682020i	$-0.761102\pi$
$547$	−34.2089	−1.46267	−0.731334	+	0.682020i	$0.761102\pi$
$548$	−78.1308	−3.33758
$549$	−8.70754	−0.371629
$550$	13.0040	0.554490
$551$	−0.517947	−0.0220653
$552$	6.60077	0.280948
$553$	70.5705	3.00097
$554$	−76.4262	−3.24704
$555$	0.0980173	0.00416060
$556$	19.3894	0.822296
$557$	18.1759	0.770136	0.385068	−	0.922888i	$-0.374178\pi$
$557$	18.1759	0.770136	0.385068	+	0.922888i	$0.374178\pi$
$558$	18.8708	0.798867
$559$	−8.76920	−0.370898
$560$	21.6565	0.915152
$561$	0.737737	0.0311473
$562$	−55.8595	−2.35629
$563$	−21.6860	−0.913957	−0.456978	−	0.889478i	$-0.651068\pi$
$563$	−21.6860	−0.913957	−0.456978	+	0.889478i	$0.651068\pi$
$564$	−5.57210	−0.234628
$565$	−2.81937	−0.118612
$566$	−66.4805	−2.79438
$567$	39.5247	1.65988
$568$	−59.5643	−2.49926
$569$	39.2724	1.64639	0.823193	−	0.567762i	$-0.192191\pi$
$569$	39.2724	1.64639	0.823193	+	0.567762i	$0.192191\pi$
$570$	1.55731	0.0652287
$571$	1.60482	0.0671597	0.0335798	−	0.999436i	$-0.489309\pi$
$571$	1.60482	0.0671597	0.0335798	+	0.999436i	$0.489309\pi$
$572$	−4.81126	−0.201169
$573$	−4.38656	−0.183251
$574$	−22.4353	−0.936432
$575$	26.1218	1.08935
$576$	−11.0165	−0.459020
$577$	−33.8644	−1.40979	−0.704897	−	0.709310i	$-0.749007\pi$
$577$	−33.8644	−1.40979	−0.704897	+	0.709310i	$0.749007\pi$
$578$	3.01809	0.125536
$579$	1.26508	0.0525748
$580$	0.223390	0.00927577
$581$	−1.02164	−0.0423848
$582$	−4.81283	−0.199498
$583$	−11.9699	−0.495742
$584$	47.0302	1.94612
$585$	1.62096	0.0670184
$586$	−67.5170	−2.78910
$587$	−21.8642	−0.902432	−0.451216	−	0.892415i	$-0.649010\pi$
$587$	−21.8642	−0.902432	−0.451216	+	0.892415i	$0.649010\pi$
$588$	10.8069	0.445671
$589$	−15.1541	−0.624415
$590$	10.0939	0.415560
$591$	−1.93426	−0.0795648
$592$	8.40065	0.345265
$593$	−18.7084	−0.768262	−0.384131	−	0.923279i	$-0.625499\pi$
$593$	−18.7084	−0.768262	−0.384131	+	0.923279i	$0.625499\pi$
$594$	2.85704	0.117226
$595$	10.2571	0.420498
$596$	48.5259	1.98770
$597$	1.77594	0.0726842
$598$	−13.8120	−0.564813
$599$	36.0591	1.47333	0.736667	−	0.676255i	$-0.236398\pi$
$599$	36.0591	1.47333	0.736667	+	0.676255i	$0.236398\pi$
$600$	5.52380	0.225508
$601$	−22.1769	−0.904613	−0.452306	−	0.891863i	$-0.649399\pi$
$601$	−22.1769	−0.904613	−0.452306	+	0.891863i	$0.649399\pi$
$602$	−106.914	−4.35751
$603$	22.2117	0.904528
$604$	−83.4941	−3.39733
$605$	−5.60499	−0.227875
$606$	7.27766	0.295635
$607$	−32.9213	−1.33623	−0.668117	−	0.744057i	$-0.732899\pi$
$607$	−32.9213	−1.33623	−0.668117	+	0.744057i	$0.732899\pi$
$608$	48.9239	1.98413
$609$	0.0655037	0.00265434
$610$	−4.31005	−0.174509
$611$	6.65616	0.269279
$612$	−55.0824	−2.22658
$613$	−32.7924	−1.32447	−0.662236	−	0.749295i	$-0.730392\pi$
$613$	−32.7924	−1.32447	−0.662236	+	0.749295i	$0.730392\pi$
$614$	−69.1656	−2.79129
$615$	0.188297	0.00759286
$616$	−33.4872	−1.34924
$617$	13.5661	0.546151	0.273075	−	0.961993i	$-0.411959\pi$
$617$	13.5661	0.546151	0.273075	+	0.961993i	$0.411959\pi$
$618$	−2.35440	−0.0947080
$619$	15.8168	0.635733	0.317866	−	0.948136i	$-0.397034\pi$
$619$	15.8168	0.635733	0.317866	+	0.948136i	$0.397034\pi$
$620$	6.53595	0.262490
$621$	5.73911	0.230302
$622$	71.9187	2.88368
$623$	−40.3799	−1.61779
$624$	−1.38449	−0.0554239
$625$	20.2371	0.809483
$626$	−25.5160	−1.01982
$627$	−1.14148	−0.0455862
$628$	−43.8608	−1.75024
$629$	3.97877	0.158644
$630$	19.7628	0.787369
$631$	−11.3506	−0.451861	−0.225931	−	0.974143i	$-0.572542\pi$
$631$	−11.3506	−0.451861	−0.225931	+	0.974143i	$0.572542\pi$
$632$	−107.089	−4.25977
$633$	−2.03505	−0.0808861
$634$	43.8055	1.73974
$635$	−11.0056	−0.436745
$636$	−8.90653	−0.353167
$637$	−12.9095	−0.511491
$638$	−0.234004	−0.00926432
$639$	−25.7660	−1.01929
$640$	3.60187	0.142376
$641$	39.9082	1.57628	0.788140	−	0.615496i	$-0.211044\pi$
$641$	39.9082	1.57628	0.788140	+	0.615496i	$0.211044\pi$
$642$	1.43820	0.0567612
$643$	−6.10439	−0.240733	−0.120367	−	0.992729i	$-0.538407\pi$
$643$	−6.10439	−0.240733	−0.120367	+	0.992729i	$0.538407\pi$
$644$	−117.832	−4.64323
$645$	0.897319	0.0353319
$646$	63.2152	2.48717
$647$	−9.17632	−0.360759	−0.180379	−	0.983597i	$-0.557733\pi$
$647$	−9.17632	−0.360759	−0.180379	+	0.983597i	$0.557733\pi$
$648$	−59.9777	−2.35615
$649$	−7.39862	−0.290421
$650$	−11.5584	−0.453359
$651$	1.91651	0.0751139
$652$	4.66069	0.182527
$653$	41.5967	1.62780	0.813902	−	0.581002i	$-0.197339\pi$
$653$	41.5967	1.62780	0.813902	+	0.581002i	$0.197339\pi$
$654$	−1.26365	−0.0494125
$655$	−6.80806	−0.266013
$656$	16.1381	0.630088
$657$	20.3441	0.793698
$658$	81.1522	3.16364
$659$	−7.34953	−0.286297	−0.143148	−	0.989701i	$-0.545723\pi$
$659$	−7.34953	−0.286297	−0.143148	+	0.989701i	$0.545723\pi$
$660$	0.492318	0.0191634
$661$	−41.1229	−1.59950	−0.799748	−	0.600336i	$-0.795033\pi$
$661$	−41.1229	−1.59950	−0.799748	+	0.600336i	$0.795033\pi$
$662$	74.8872	2.91058
$663$	−0.655730	−0.0254665
$664$	1.55031	0.0601638
$665$	−15.8704	−0.615428
$666$	7.66610	0.297055
$667$	−0.470059	−0.0182007
$668$	15.9506	0.617149
$669$	−3.55635	−0.137496
$670$	10.9943	0.424747
$671$	3.15917	0.121958
$672$	−6.18730	−0.238680
$673$	−16.9596	−0.653746	−0.326873	−	0.945068i	$-0.605995\pi$
$673$	−16.9596	−0.653746	−0.326873	+	0.945068i	$0.605995\pi$
$674$	−54.2873	−2.09107
$675$	4.80272	0.184857
$676$	−56.3125	−2.16587
$677$	20.3255	0.781173	0.390586	−	0.920566i	$-0.372272\pi$
$677$	20.3255	0.781173	0.390586	+	0.920566i	$0.372272\pi$
$678$	2.19751	0.0843949
$679$	49.0470	1.88225
$680$	−15.5648	−0.596883
$681$	0.827310	0.0317026
$682$	−6.84651	−0.262166
$683$	23.9182	0.915205	0.457603	−	0.889157i	$-0.348708\pi$
$683$	23.9182	0.915205	0.457603	+	0.889157i	$0.348708\pi$
$684$	85.2272	3.25874
$685$	−9.55023	−0.364895
$686$	−75.6421	−2.88803
$687$	−0.213097	−0.00813015
$688$	76.9054	2.93199
$689$	10.6393	0.405325
$690$	1.41333	0.0538044
$691$	−15.8673	−0.603622	−0.301811	−	0.953368i	$-0.597591\pi$
$691$	−15.8673	−0.603622	−0.301811	+	0.953368i	$0.597591\pi$
$692$	−13.6987	−0.520745
$693$	−14.4857	−0.550267
$694$	−83.9816	−3.18790
$695$	2.37005	0.0899010
$696$	−0.0994000	−0.00376775
$697$	7.64343	0.289516
$698$	−7.68425	−0.290853
$699$	−4.04980	−0.153178
$700$	−98.6066	−3.72698
$701$	−36.3796	−1.37404	−0.687019	−	0.726640i	$-0.741081\pi$
$701$	−36.3796	−1.37404	−0.687019	+	0.726640i	$0.741081\pi$
$702$	−2.53945	−0.0958454
$703$	−6.15621	−0.232186
$704$	3.99688	0.150638
$705$	−0.681099	−0.0256517
$706$	7.97780	0.300248
$707$	−74.1658	−2.78929
$708$	−5.50515	−0.206896
$709$	−22.2743	−0.836530	−0.418265	−	0.908325i	$-0.637362\pi$
$709$	−22.2743	−0.836530	−0.418265	+	0.908325i	$0.637362\pi$
$710$	−12.7536	−0.478635
$711$	−46.3239	−1.73728
$712$	61.2755	2.29640
$713$	−13.7530	−0.515054
$714$	−7.99469	−0.299194
$715$	−0.588099	−0.0219936
$716$	11.3586	0.424489
$717$	2.54311	0.0949743
$718$	14.1689	0.528780
$719$	−12.7020	−0.473705	−0.236852	−	0.971546i	$-0.576116\pi$
$719$	−12.7020	−0.473705	−0.236852	+	0.971546i	$0.576116\pi$
$720$	−14.2157	−0.529789
$721$	23.9935	0.893563
$722$	−48.7750	−1.81522
$723$	3.19577	0.118852
$724$	58.7186	2.18226
$725$	−0.393364	−0.0146092
$726$	4.36871	0.162138
$727$	14.7855	0.548363	0.274181	−	0.961678i	$-0.411593\pi$
$727$	14.7855	0.548363	0.274181	+	0.961678i	$0.411593\pi$
$728$	29.7648	1.10316
$729$	−25.4146	−0.941282
$730$	10.0699	0.372703
$731$	36.4244	1.34721
$732$	2.35067	0.0868833
$733$	−9.37173	−0.346153	−0.173076	−	0.984908i	$-0.555371\pi$
$733$	−9.37173	−0.346153	−0.173076	+	0.984908i	$0.555371\pi$
$734$	−13.8584	−0.511522
$735$	1.32097	0.0487249
$736$	44.4004	1.63662
$737$	−8.05858	−0.296842
$738$	14.7270	0.542108
$739$	−0.704196	−0.0259043	−0.0129521	−	0.999916i	$-0.504123\pi$
$739$	−0.704196	−0.0259043	−0.0129521	+	0.999916i	$0.504123\pi$
$740$	2.65517	0.0976059
$741$	1.01459	0.0372719
$742$	129.715	4.76198
$743$	−53.1699	−1.95061	−0.975307	−	0.220852i	$-0.929116\pi$
$743$	−53.1699	−1.95061	−0.975307	+	0.220852i	$0.929116\pi$
$744$	−2.90825	−0.106622
$745$	5.93151	0.217314
$746$	−69.0143	−2.52679
$747$	0.670626	0.0245369
$748$	19.9844	0.730702
$749$	−14.6565	−0.535538
$750$	2.44756	0.0893723
$751$	23.2027	0.846679	0.423340	−	0.905971i	$-0.360858\pi$
$751$	23.2027	0.846679	0.423340	+	0.905971i	$0.360858\pi$
$752$	−58.3742	−2.12869
$753$	−2.23731	−0.0815321
$754$	0.207992	0.00757463
$755$	−10.2058	−0.371428
$756$	−21.6644	−0.787927
$757$	−26.6167	−0.967400	−0.483700	−	0.875234i	$-0.660707\pi$
$757$	−26.6167	−0.967400	−0.483700	+	0.875234i	$0.660707\pi$
$758$	36.5806	1.32867
$759$	−1.03594	−0.0376021
$760$	24.0829	0.873579
$761$	−3.49538	−0.126708	−0.0633538	−	0.997991i	$-0.520180\pi$
$761$	−3.49538	−0.126708	−0.0633538	+	0.997991i	$0.520180\pi$
$762$	8.57814	0.310753
$763$	12.8777	0.466204
$764$	−118.826	−4.29899
$765$	−6.73294	−0.243430
$766$	88.5677	3.20008
$767$	6.57618	0.237452
$768$	−4.08362	−0.147355
$769$	−5.38770	−0.194285	−0.0971427	−	0.995270i	$-0.530970\pi$
$769$	−5.38770	−0.194285	−0.0971427	+	0.995270i	$0.530970\pi$
$770$	−7.17012	−0.258393
$771$	−2.51687	−0.0906429
$772$	34.2694	1.23338
$773$	23.6953	0.852261	0.426131	−	0.904662i	$-0.359876\pi$
$773$	23.6953	0.852261	0.426131	+	0.904662i	$0.359876\pi$
$774$	70.1808	2.52260
$775$	−11.5091	−0.413418
$776$	−74.4276	−2.67179
$777$	0.778563	0.0279308
$778$	36.7897	1.31898
$779$	−11.8264	−0.423726
$780$	−0.437591	−0.0156683
$781$	9.34813	0.334502
$782$	57.3704	2.05156
$783$	−0.0864243	−0.00308855
$784$	113.215	4.04340
$785$	−5.36127	−0.191352
$786$	5.30643	0.189274
$787$	7.67087	0.273437	0.136718	−	0.990610i	$-0.456344\pi$
$787$	7.67087	0.273437	0.136718	+	0.990610i	$0.456344\pi$
$788$	−52.3967	−1.86656
$789$	−2.27299	−0.0809206
$790$	−22.9294	−0.815790
$791$	−22.3946	−0.796260
$792$	21.9817	0.781085
$793$	−2.80800	−0.0997149
$794$	−83.7845	−2.97340
$795$	−1.08868	−0.0386115
$796$	48.1079	1.70514
$797$	27.2132	0.963940	0.481970	−	0.876188i	$-0.339921\pi$
$797$	27.2132	0.963940	0.481970	+	0.876188i	$0.339921\pi$
$798$	12.3699	0.437890
$799$	−27.6475	−0.978099
$800$	37.1561	1.31367
$801$	26.5062	0.936551
$802$	39.1761	1.38336
$803$	−7.38101	−0.260470
$804$	−5.99622	−0.211470
$805$	−14.4031	−0.507641
$806$	6.08545	0.214351
$807$	3.67214	0.129265
$808$	112.545	3.95931
$809$	−4.21648	−0.148244	−0.0741218	−	0.997249i	$-0.523615\pi$
$809$	−4.21648	−0.148244	−0.0741218	+	0.997249i	$0.523615\pi$
$810$	−12.8421	−0.451227
$811$	3.83535	0.134677	0.0673387	−	0.997730i	$-0.478549\pi$
$811$	3.83535	0.134677	0.0673387	+	0.997730i	$0.478549\pi$
$812$	1.77441	0.0622697
$813$	−0.0856511	−0.00300392
$814$	−2.78133	−0.0974855
$815$	0.569694	0.0199555
$816$	5.75072	0.201315
$817$	−56.3583	−1.97173
$818$	90.6701	3.17021
$819$	12.8755	0.449906
$820$	5.10073	0.178125
$821$	8.01327	0.279665	0.139832	−	0.990175i	$-0.455344\pi$
$821$	8.01327	0.279665	0.139832	+	0.990175i	$0.455344\pi$
$822$	7.44376	0.259631
$823$	11.5420	0.402328	0.201164	−	0.979558i	$-0.435528\pi$
$823$	11.5420	0.402328	0.201164	+	0.979558i	$0.435528\pi$
$824$	−36.4094	−1.26838
$825$	−0.866915	−0.0301821
$826$	80.1771	2.78972
$827$	−39.2979	−1.36652	−0.683261	−	0.730174i	$-0.739439\pi$
$827$	−39.2979	−1.36652	−0.683261	+	0.730174i	$0.739439\pi$
$828$	77.3473	2.68800
$829$	47.6179	1.65384	0.826918	−	0.562322i	$-0.190092\pi$
$829$	47.6179	1.65384	0.826918	+	0.562322i	$0.190092\pi$
$830$	0.331946	0.0115220
$831$	5.09499	0.176743
$832$	−3.55259	−0.123164
$833$	53.6217	1.85788
$834$	−1.84729	−0.0639665
$835$	1.94971	0.0674724
$836$	−30.9212	−1.06943
$837$	−2.52861	−0.0874014
$838$	−39.4169	−1.36163
$839$	46.7755	1.61487	0.807435	−	0.589957i	$-0.200855\pi$
$839$	46.7755	1.61487	0.807435	+	0.589957i	$0.200855\pi$
$840$	−3.04571	−0.105087
$841$	−28.9929	−0.999756
$842$	59.2094	2.04049
$843$	3.72391	0.128258
$844$	−55.1271	−1.89755
$845$	−6.88330	−0.236793
$846$	−53.2699	−1.83146
$847$	−44.5211	−1.52976
$848$	−93.3061	−3.20415
$849$	4.43196	0.152104
$850$	48.0099	1.64673
$851$	−5.58702	−0.191521
$852$	6.95574	0.238300
$853$	2.96230	0.101427	0.0507136	−	0.998713i	$-0.483850\pi$
$853$	2.96230	0.101427	0.0507136	+	0.998713i	$0.483850\pi$
$854$	−34.2352	−1.17150
$855$	10.4177	0.356276
$856$	22.2409	0.760178
$857$	36.8480	1.25870	0.629352	−	0.777120i	$-0.283320\pi$
$857$	36.8480	1.25870	0.629352	+	0.777120i	$0.283320\pi$
$858$	0.458384	0.0156490
$859$	−47.6517	−1.62586	−0.812928	−	0.582365i	$-0.802128\pi$
$859$	−47.6517	−1.62586	−0.812928	+	0.582365i	$0.802128\pi$
$860$	24.3073	0.828871
$861$	1.49566	0.0509720
$862$	2.74008	0.0933277
$863$	−27.8367	−0.947571	−0.473786	−	0.880640i	$-0.657113\pi$
$863$	−27.8367	−0.947571	−0.473786	+	0.880640i	$0.657113\pi$
$864$	8.16341	0.277725
$865$	−1.67444	−0.0569327
$866$	67.4890	2.29337
$867$	−0.201202	−0.00683319
$868$	51.9159	1.76214
$869$	16.8067	0.570129
$870$	−0.0212831	−0.000721563 0
$871$	7.16279	0.242702
$872$	−19.5416	−0.661761
$873$	−32.1955	−1.08965
$874$	−88.7674	−3.00260
$875$	−24.9428	−0.843221
$876$	−5.49205	−0.185559
$877$	−24.8057	−0.837628	−0.418814	−	0.908072i	$-0.637554\pi$
$877$	−24.8057	−0.837628	−0.418814	+	0.908072i	$0.637554\pi$
$878$	35.5229	1.19884
$879$	4.50105	0.151817
$880$	5.15759	0.173862
$881$	−43.3942	−1.46199	−0.730994	−	0.682384i	$-0.760943\pi$
$881$	−43.3942	−1.46199	−0.730994	+	0.682384i	$0.760943\pi$
$882$	103.316	3.47882
$883$	46.2636	1.55689	0.778447	−	0.627710i	$-0.216008\pi$
$883$	46.2636	1.55689	0.778447	+	0.627710i	$0.216008\pi$
$884$	−17.7629	−0.597432
$885$	−0.672916	−0.0226198
$886$	15.7576	0.529387
$887$	40.5168	1.36042	0.680210	−	0.733017i	$-0.261889\pi$
$887$	40.5168	1.36042	0.680210	+	0.733017i	$0.261889\pi$
$888$	−1.18145	−0.0396468
$889$	−87.4189	−2.93194
$890$	13.1200	0.439784
$891$	9.41301	0.315348
$892$	−96.3372	−3.22561
$893$	42.7781	1.43151
$894$	−4.62321	−0.154623
$895$	1.38840	0.0464091
$896$	28.6101	0.955796
$897$	0.920782	0.0307440
$898$	−17.5121	−0.584385
$899$	0.207104	0.00690731
$900$	64.7274	2.15758
$901$	−44.1922	−1.47226
$902$	−5.34309	−0.177905
$903$	7.12751	0.237189
$904$	33.9832	1.13026
$905$	7.17740	0.238585
$906$	7.95475	0.264279
$907$	6.06332	0.201329	0.100665	−	0.994920i	$-0.467903\pi$
$907$	6.06332	0.201329	0.100665	+	0.994920i	$0.467903\pi$
$908$	22.4108	0.743728
$909$	48.6839	1.61474
$910$	6.37309	0.211266
$911$	46.3194	1.53463	0.767315	−	0.641270i	$-0.221592\pi$
$911$	46.3194	1.53463	0.767315	+	0.641270i	$0.221592\pi$
$912$	−8.89790	−0.294639
$913$	−0.243309	−0.00805235
$914$	−78.4378	−2.59449
$915$	0.287332	0.00949889
$916$	−5.77253	−0.190730
$917$	−54.0772	−1.78579
$918$	10.5480	0.348138
$919$	19.1858	0.632879	0.316440	−	0.948613i	$-0.397512\pi$
$919$	19.1858	0.632879	0.316440	+	0.948613i	$0.397512\pi$
$920$	21.8562	0.720579
$921$	4.61096	0.151936
$922$	16.7229	0.550739
$923$	−8.30899	−0.273494
$924$	3.91054	0.128647
$925$	−4.67545	−0.153728
$926$	−1.62176	−0.0532942
$927$	−15.7498	−0.517291
$928$	−0.668620	−0.0219485
$929$	−44.9406	−1.47445	−0.737227	−	0.675645i	$-0.763865\pi$
$929$	−44.9406	−1.47445	−0.737227	+	0.675645i	$0.763865\pi$
$930$	−0.622701	−0.0204192
$931$	−82.9670	−2.71913
$932$	−109.704	−3.59348
$933$	−4.79450	−0.156965
$934$	15.9884	0.523156
$935$	2.44277	0.0798871
$936$	−19.5382	−0.638626
$937$	15.6784	0.512192	0.256096	−	0.966651i	$-0.417564\pi$
$937$	15.6784	0.512192	0.256096	+	0.966651i	$0.417564\pi$
$938$	87.3290	2.85139
$939$	1.70104	0.0555112
$940$	−18.4501	−0.601777
$941$	−45.4152	−1.48049	−0.740247	−	0.672335i	$-0.765292\pi$
$941$	−45.4152	−1.48049	−0.740247	+	0.672335i	$0.765292\pi$
$942$	4.17875	0.136151
$943$	−10.7330	−0.349514
$944$	−57.6728	−1.87709
$945$	−2.64813	−0.0861436
$946$	−25.4622	−0.827848
$947$	−24.4477	−0.794444	−0.397222	−	0.917723i	$-0.630026\pi$
$947$	−24.4477	−0.794444	−0.397222	+	0.917723i	$0.630026\pi$
$948$	12.5055	0.406161
$949$	6.56053	0.212964
$950$	−74.2842	−2.41010
$951$	−2.92032	−0.0946978
$952$	−123.633	−4.00697
$953$	13.7474	0.445321	0.222660	−	0.974896i	$-0.428526\pi$
$953$	13.7474	0.445321	0.222660	+	0.974896i	$0.428526\pi$
$954$	−85.1474	−2.75675
$955$	−14.5246	−0.470006
$956$	68.8898	2.22805
$957$	0.0156000	0.000504277 0
$958$	91.3747	2.95218
$959$	−75.8586	−2.44960
$960$	0.363522	0.0117326
$961$	−24.9405	−0.804533
$962$	2.47215	0.0797054
$963$	9.62084	0.310027
$964$	86.5694	2.78821
$965$	4.18888	0.134845
$966$	11.2262	0.361198
$967$	18.1298	0.583014	0.291507	−	0.956569i	$-0.405843\pi$
$967$	18.1298	0.583014	0.291507	+	0.956569i	$0.405843\pi$
$968$	67.5595	2.17145
$969$	−4.21428	−0.135382
$970$	−15.9361	−0.511677
$971$	−52.4026	−1.68168	−0.840839	−	0.541285i	$-0.817938\pi$
$971$	−52.4026	−1.68168	−0.840839	+	0.541285i	$0.817938\pi$
$972$	21.3667	0.685337
$973$	18.8256	0.603520
$974$	−15.4882	−0.496274
$975$	0.770549	0.0246773
$976$	24.6260	0.788258
$977$	13.4029	0.428798	0.214399	−	0.976746i	$-0.431221\pi$
$977$	13.4029	0.428798	0.214399	+	0.976746i	$0.431221\pi$
$978$	−0.444038	−0.0141988
$979$	−9.61669	−0.307351
$980$	35.7836	1.14306
$981$	−8.45318	−0.269889
$982$	−82.1664	−2.62204
$983$	−0.00197392	−6.29583e−5 0	−3.14791e−5	−	1.00000i	$-0.500010\pi$
$983$	−0.00197392	−6.29583e−5 0	−3.14791e−5		1.00000i	$0.500010\pi$
$984$	−2.26963	−0.0723531
$985$	−6.40465	−0.204069
$986$	−0.863932	−0.0275132
$987$	−5.41005	−0.172204
$988$	27.4840	0.874382
$989$	−51.1475	−1.62640
$990$	4.70661	0.149586
$991$	−20.2231	−0.642408	−0.321204	−	0.947010i	$-0.604088\pi$
$991$	−20.2231	−0.642408	−0.321204	+	0.947010i	$0.604088\pi$
$992$	−19.5625	−0.621110
$993$	−4.99240	−0.158429
$994$	−101.304	−3.21315
$995$	5.88042	0.186422
$996$	−0.181041	−0.00573650
$997$	53.7890	1.70351	0.851757	−	0.523937i	$-0.175537\pi$
$997$	53.7890	1.70351	0.851757	+	0.523937i	$0.175537\pi$
$998$	−22.3436	−0.707274
$999$	−1.02722	−0.0324999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.7	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.7	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58083 q^{2} +0.172052 q^{3} +4.66069 q^{4} +0.569694 q^{5} -0.444038 q^{6} +4.52515 q^{7} -6.86679 q^{8} -2.97040 q^{9} +O(q^{10})\)	\(q-2.58083 q^{2} +0.172052 q^{3} +4.66069 q^{4} +0.569694 q^{5} -0.444038 q^{6} +4.52515 q^{7} -6.86679 q^{8} -2.97040 q^{9} -1.47028 q^{10} +1.07769 q^{11} +0.801883 q^{12} -0.957891 q^{13} -11.6786 q^{14} +0.0980173 q^{15} +8.40065 q^{16} +3.97877 q^{17} +7.66610 q^{18} -6.15621 q^{19} +2.65517 q^{20} +0.778563 q^{21} -2.78133 q^{22} -5.58702 q^{23} -1.18145 q^{24} -4.67545 q^{25} +2.47215 q^{26} -1.02722 q^{27} +21.0903 q^{28} +0.0841341 q^{29} -0.252966 q^{30} +2.46160 q^{31} -7.94707 q^{32} +0.185419 q^{33} -10.2685 q^{34} +2.57795 q^{35} -13.8441 q^{36} +1.00000 q^{37} +15.8881 q^{38} -0.164807 q^{39} -3.91197 q^{40} +1.92106 q^{41} -2.00934 q^{42} +9.15470 q^{43} +5.02276 q^{44} -1.69222 q^{45} +14.4192 q^{46} -6.94877 q^{47} +1.44535 q^{48} +13.4770 q^{49} +12.0665 q^{50} +0.684556 q^{51} -4.46443 q^{52} -11.1070 q^{53} +2.65109 q^{54} +0.613952 q^{55} -31.0732 q^{56} -1.05919 q^{57} -0.217136 q^{58} -6.86528 q^{59} +0.456828 q^{60} +2.93144 q^{61} -6.35297 q^{62} -13.4415 q^{63} +3.70876 q^{64} -0.545705 q^{65} -0.478534 q^{66} -7.47767 q^{67} +18.5438 q^{68} -0.961260 q^{69} -6.65325 q^{70} +8.67426 q^{71} +20.3971 q^{72} -6.84894 q^{73} -2.58083 q^{74} -0.804423 q^{75} -28.6922 q^{76} +4.87669 q^{77} +0.425340 q^{78} +15.5952 q^{79} +4.78580 q^{80} +8.73446 q^{81} -4.95792 q^{82} -0.225770 q^{83} +3.62864 q^{84} +2.26668 q^{85} -23.6267 q^{86} +0.0144755 q^{87} -7.40025 q^{88} -8.92345 q^{89} +4.36733 q^{90} -4.33460 q^{91} -26.0394 q^{92} +0.423524 q^{93} +17.9336 q^{94} -3.50716 q^{95} -1.36731 q^{96} +10.8388 q^{97} -34.7818 q^{98} -3.20116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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