LMFDB - Embedded newform 8047.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80247 q^{2} -1.33128 q^{3} +5.85385 q^{4} -2.29720 q^{5} +3.73087 q^{6} -2.08383 q^{7} -10.8003 q^{8} -1.22769 q^{9} +O(q^{10})$	\(q-2.80247 q^{2} -1.33128 q^{3} +5.85385 q^{4} -2.29720 q^{5} +3.73087 q^{6} -2.08383 q^{7} -10.8003 q^{8} -1.22769 q^{9} +6.43783 q^{10} +6.42747 q^{11} -7.79311 q^{12} -1.00000 q^{13} +5.83989 q^{14} +3.05821 q^{15} +18.5599 q^{16} -6.66259 q^{17} +3.44058 q^{18} -0.748871 q^{19} -13.4474 q^{20} +2.77417 q^{21} -18.0128 q^{22} -0.0260822 q^{23} +14.3782 q^{24} +0.277110 q^{25} +2.80247 q^{26} +5.62824 q^{27} -12.1985 q^{28} +3.74812 q^{29} -8.57055 q^{30} -1.10126 q^{31} -30.4129 q^{32} -8.55676 q^{33} +18.6717 q^{34} +4.78697 q^{35} -7.18674 q^{36} +4.49605 q^{37} +2.09869 q^{38} +1.33128 q^{39} +24.8104 q^{40} -4.93162 q^{41} -7.77452 q^{42} +5.60500 q^{43} +37.6254 q^{44} +2.82025 q^{45} +0.0730947 q^{46} -3.47413 q^{47} -24.7084 q^{48} -2.65764 q^{49} -0.776592 q^{50} +8.86977 q^{51} -5.85385 q^{52} -2.56712 q^{53} -15.7730 q^{54} -14.7652 q^{55} +22.5061 q^{56} +0.996957 q^{57} -10.5040 q^{58} -3.51132 q^{59} +17.9023 q^{60} -5.04834 q^{61} +3.08625 q^{62} +2.55831 q^{63} +48.1116 q^{64} +2.29720 q^{65} +23.9801 q^{66} -9.17420 q^{67} -39.0018 q^{68} +0.0347227 q^{69} -13.4154 q^{70} -4.47916 q^{71} +13.2595 q^{72} +13.2759 q^{73} -12.6001 q^{74} -0.368910 q^{75} -4.38378 q^{76} -13.3938 q^{77} -3.73087 q^{78} +5.67905 q^{79} -42.6357 q^{80} -3.80968 q^{81} +13.8207 q^{82} -5.05656 q^{83} +16.2396 q^{84} +15.3053 q^{85} -15.7079 q^{86} -4.98979 q^{87} -69.4187 q^{88} +5.76576 q^{89} -7.90369 q^{90} +2.08383 q^{91} -0.152681 q^{92} +1.46608 q^{93} +9.73617 q^{94} +1.72030 q^{95} +40.4881 q^{96} -2.50575 q^{97} +7.44795 q^{98} -7.89097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * 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 $

$2$	−2.80247	−1.98165	−0.990824	−	0.135161i	$-0.956845\pi$
$2$	−2.80247	−1.98165	−0.990824	+	0.135161i	$0.956845\pi$
$3$	−1.33128	−0.768615	−0.384307	−	0.923205i	$-0.625560\pi$
$3$	−1.33128	−0.768615	−0.384307	+	0.923205i	$0.625560\pi$
$4$	5.85385	2.92693
$5$	−2.29720	−1.02734	−0.513669	−	0.857989i	$-0.671714\pi$
$5$	−2.29720	−1.02734	−0.513669	+	0.857989i	$0.671714\pi$
$6$	3.73087	1.52312
$7$	−2.08383	−0.787615	−0.393808	−	0.919193i	$-0.628842\pi$
$7$	−2.08383	−0.787615	−0.393808	+	0.919193i	$0.628842\pi$
$8$	−10.8003	−3.81849
$9$	−1.22769	−0.409231
$10$	6.43783	2.03582
$11$	6.42747	1.93795	0.968977	−	0.247150i	$-0.0794940\pi$
$11$	6.42747	1.93795	0.968977	+	0.247150i	$0.0794940\pi$
$12$	−7.79311	−2.24968
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.83989	1.56078
$15$	3.05821	0.789627
$16$	18.5599	4.63997
$17$	−6.66259	−1.61592	−0.807958	−	0.589240i	$-0.799427\pi$
$17$	−6.66259	−1.61592	−0.807958	+	0.589240i	$0.799427\pi$
$18$	3.44058	0.810952
$19$	−0.748871	−0.171803	−0.0859014	−	0.996304i	$-0.527377\pi$
$19$	−0.748871	−0.171803	−0.0859014	+	0.996304i	$0.527377\pi$
$20$	−13.4474	−3.00694
$21$	2.77417	0.605373
$22$	−18.0128	−3.84034
$23$	−0.0260822	−0.00543852	−0.00271926	−	0.999996i	$-0.500866\pi$
$23$	−0.0260822	−0.00543852	−0.00271926	+	0.999996i	$0.500866\pi$
$24$	14.3782	2.93495
$25$	0.277110	0.0554219
$26$	2.80247	0.549610
$27$	5.62824	1.08316
$28$	−12.1985	−2.30529
$29$	3.74812	0.696008	0.348004	−	0.937493i	$-0.386860\pi$
$29$	3.74812	0.696008	0.348004	+	0.937493i	$0.386860\pi$
$30$	−8.57055	−1.56476
$31$	−1.10126	−0.197792	−0.0988961	−	0.995098i	$-0.531531\pi$
$31$	−1.10126	−0.197792	−0.0988961	+	0.995098i	$0.531531\pi$
$32$	−30.4129	−5.37629
$33$	−8.55676	−1.48954
$34$	18.6717	3.20217
$35$	4.78697	0.809146
$36$	−7.18674	−1.19779
$37$	4.49605	0.739147	0.369573	−	0.929202i	$-0.379504\pi$
$37$	4.49605	0.739147	0.369573	+	0.929202i	$0.379504\pi$
$38$	2.09869	0.340452
$39$	1.33128	0.213175
$40$	24.8104	3.92287
$41$	−4.93162	−0.770190	−0.385095	−	0.922877i	$-0.625831\pi$
$41$	−4.93162	−0.770190	−0.385095	+	0.922877i	$0.625831\pi$
$42$	−7.77452	−1.19963
$43$	5.60500	0.854755	0.427378	−	0.904073i	$-0.359438\pi$
$43$	5.60500	0.854755	0.427378	+	0.904073i	$0.359438\pi$
$44$	37.6254	5.67225
$45$	2.82025	0.420419
$46$	0.0730947	0.0107772
$47$	−3.47413	−0.506755	−0.253377	−	0.967368i	$-0.581541\pi$
$47$	−3.47413	−0.506755	−0.253377	+	0.967368i	$0.581541\pi$
$48$	−24.7084	−3.56635
$49$	−2.65764	−0.379662
$50$	−0.776592	−0.109827
$51$	8.86977	1.24202
$52$	−5.85385	−0.811783
$53$	−2.56712	−0.352622	−0.176311	−	0.984335i	$-0.556416\pi$
$53$	−2.56712	−0.352622	−0.176311	+	0.984335i	$0.556416\pi$
$54$	−15.7730	−2.14643
$55$	−14.7652	−1.99093
$56$	22.5061	3.00750
$57$	0.996957	0.132050
$58$	−10.5040	−1.37924
$59$	−3.51132	−0.457135	−0.228568	−	0.973528i	$-0.573404\pi$
$59$	−3.51132	−0.457135	−0.228568	+	0.973528i	$0.573404\pi$
$60$	17.9023	2.31118
$61$	−5.04834	−0.646374	−0.323187	−	0.946335i	$-0.604754\pi$
$61$	−5.04834	−0.646374	−0.323187	+	0.946335i	$0.604754\pi$
$62$	3.08625	0.391954
$63$	2.55831	0.322317
$64$	48.1116	6.01395
$65$	2.29720	0.284932
$66$	23.9801	2.95174
$67$	−9.17420	−1.12081	−0.560404	−	0.828220i	$-0.689354\pi$
$67$	−9.17420	−1.12081	−0.560404	+	0.828220i	$0.689354\pi$
$68$	−39.0018	−4.72967
$69$	0.0347227	0.00418012
$70$	−13.4154	−1.60344
$71$	−4.47916	−0.531579	−0.265789	−	0.964031i	$-0.585633\pi$
$71$	−4.47916	−0.531579	−0.265789	+	0.964031i	$0.585633\pi$
$72$	13.2595	1.56264
$73$	13.2759	1.55382	0.776911	−	0.629610i	$-0.216785\pi$
$73$	13.2759	1.55382	0.776911	+	0.629610i	$0.216785\pi$
$74$	−12.6001	−1.46473
$75$	−0.368910	−0.0425981
$76$	−4.38378	−0.502854
$77$	−13.3938	−1.52636
$78$	−3.73087	−0.422438
$79$	5.67905	0.638944	0.319472	−	0.947596i	$-0.396495\pi$
$79$	5.67905	0.638944	0.319472	+	0.947596i	$0.396495\pi$
$80$	−42.6357	−4.76681
$81$	−3.80968	−0.423298
$82$	13.8207	1.52624
$83$	−5.05656	−0.555030	−0.277515	−	0.960721i	$-0.589511\pi$
$83$	−5.05656	−0.555030	−0.277515	+	0.960721i	$0.589511\pi$
$84$	16.2396	1.77188
$85$	15.3053	1.66009
$86$	−15.7079	−1.69382
$87$	−4.98979	−0.534962
$88$	−69.4187	−7.40005
$89$	5.76576	0.611169	0.305585	−	0.952165i	$-0.401148\pi$
$89$	5.76576	0.611169	0.305585	+	0.952165i	$0.401148\pi$
$90$	−7.90369	−0.833122
$91$	2.08383	0.218445
$92$	−0.152681	−0.0159181
$93$	1.46608	0.152026
$94$	9.73617	1.00421
$95$	1.72030	0.176499
$96$	40.4881	4.13230
$97$	−2.50575	−0.254421	−0.127210	−	0.991876i	$-0.540602\pi$
$97$	−2.50575	−0.254421	−0.127210	+	0.991876i	$0.540602\pi$
$98$	7.44795	0.752357
$99$	−7.89097	−0.793072
$100$	1.62216	0.162216
$101$	−6.47522	−0.644308	−0.322154	−	0.946687i	$-0.604407\pi$
$101$	−6.47522	−0.644308	−0.322154	+	0.946687i	$0.604407\pi$
$102$	−24.8573	−2.46124
$103$	9.64912	0.950756	0.475378	−	0.879782i	$-0.342311\pi$
$103$	9.64912	0.950756	0.475378	+	0.879782i	$0.342311\pi$
$104$	10.8003	1.05906
$105$	−6.37280	−0.621922
$106$	7.19429	0.698772
$107$	−0.988966	−0.0956070	−0.0478035	−	0.998857i	$-0.515222\pi$
$107$	−0.988966	−0.0956070	−0.0478035	+	0.998857i	$0.515222\pi$
$108$	32.9469	3.17032
$109$	9.78806	0.937526	0.468763	−	0.883324i	$-0.344700\pi$
$109$	9.78806	0.937526	0.468763	+	0.883324i	$0.344700\pi$
$110$	41.3789	3.94533
$111$	−5.98551	−0.568119
$112$	−38.6757	−3.65451
$113$	12.8803	1.21168	0.605839	−	0.795588i	$-0.292838\pi$
$113$	12.8803	1.21168	0.605839	+	0.795588i	$0.292838\pi$
$114$	−2.79394	−0.261677
$115$	0.0599160	0.00558719
$116$	21.9409	2.03716
$117$	1.22769	0.113500
$118$	9.84038	0.905880
$119$	13.8837	1.27272
$120$	−33.0296	−3.01518
$121$	30.3123	2.75567
$122$	14.1478	1.28088
$123$	6.56537	0.591979
$124$	−6.44661	−0.578923
$125$	10.8494	0.970400
$126$	−7.16960	−0.638718
$127$	8.20734	0.728283	0.364142	−	0.931344i	$-0.381362\pi$
$127$	8.20734	0.728283	0.364142	+	0.931344i	$0.381362\pi$
$128$	−74.0056	−6.54123
$129$	−7.46183	−0.656977
$130$	−6.43783	−0.564635
$131$	13.6054	1.18871	0.594354	−	0.804203i	$-0.297408\pi$
$131$	13.6054	1.18871	0.594354	+	0.804203i	$0.297408\pi$
$132$	−50.0900	−4.35977
$133$	1.56052	0.135314
$134$	25.7104	2.22104
$135$	−12.9292	−1.11277
$136$	71.9581	6.17035
$137$	−7.36759	−0.629456	−0.314728	−	0.949182i	$-0.601913\pi$
$137$	−7.36759	−0.629456	−0.314728	+	0.949182i	$0.601913\pi$
$138$	−0.0973095	−0.00828353
$139$	−6.46106	−0.548020	−0.274010	−	0.961727i	$-0.588350\pi$
$139$	−6.46106	−0.548020	−0.274010	+	0.961727i	$0.588350\pi$
$140$	28.0222	2.36831
$141$	4.62504	0.389499
$142$	12.5527	1.05340
$143$	−6.42747	−0.537492
$144$	−22.7859	−1.89882
$145$	−8.61016	−0.715035
$146$	−37.2053	−3.07913
$147$	3.53806	0.291814
$148$	26.3192	2.16343
$149$	−8.69977	−0.712713	−0.356356	−	0.934350i	$-0.615981\pi$
$149$	−8.69977	−0.712713	−0.356356	+	0.934350i	$0.615981\pi$
$150$	1.03386	0.0844144
$151$	1.57826	0.128437	0.0642185	−	0.997936i	$-0.479545\pi$
$151$	1.57826	0.128437	0.0642185	+	0.997936i	$0.479545\pi$
$152$	8.08804	0.656027
$153$	8.17962	0.661283
$154$	37.5357	3.02471
$155$	2.52981	0.203199
$156$	7.79311	0.623948
$157$	10.8210	0.863609	0.431804	−	0.901967i	$-0.357877\pi$
$157$	10.8210	0.863609	0.431804	+	0.901967i	$0.357877\pi$
$158$	−15.9154	−1.26616
$159$	3.41756	0.271030
$160$	69.8644	5.52327
$161$	0.0543510	0.00428346
$162$	10.6765	0.838828
$163$	−18.9715	−1.48596	−0.742982	−	0.669311i	$-0.766589\pi$
$163$	−18.9715	−1.48596	−0.742982	+	0.669311i	$0.766589\pi$
$164$	−28.8690	−2.25429
$165$	19.6566	1.53026
$166$	14.1709	1.09987
$167$	−17.6007	−1.36198	−0.680992	−	0.732291i	$-0.738451\pi$
$167$	−17.6007	−1.36198	−0.680992	+	0.732291i	$0.738451\pi$
$168$	−29.9619	−2.31161
$169$	1.00000	0.0769231
$170$	−42.8926	−3.28971
$171$	0.919384	0.0703071
$172$	32.8109	2.50180
$173$	−5.17961	−0.393798	−0.196899	−	0.980424i	$-0.563087\pi$
$173$	−5.17961	−0.393798	−0.196899	+	0.980424i	$0.563087\pi$
$174$	13.9837	1.06011
$175$	−0.577450	−0.0436512
$176$	119.293	8.99205
$177$	4.67455	0.351361
$178$	−16.1584	−1.21112
$179$	−16.6824	−1.24690	−0.623452	−	0.781862i	$-0.714270\pi$
$179$	−16.6824	−1.24690	−0.623452	+	0.781862i	$0.714270\pi$
$180$	16.5094	1.23053
$181$	19.6357	1.45951	0.729756	−	0.683708i	$-0.239634\pi$
$181$	19.6357	1.45951	0.729756	+	0.683708i	$0.239634\pi$
$182$	−5.83989	−0.432881
$183$	6.72075	0.496812
$184$	0.281696	0.0207669
$185$	−10.3283	−0.759353
$186$	−4.10866	−0.301262
$187$	−42.8236	−3.13157
$188$	−20.3371	−1.48323
$189$	−11.7283	−0.853110
$190$	−4.82110	−0.349759
$191$	14.8214	1.07244	0.536220	−	0.844078i	$-0.319852\pi$
$191$	14.8214	1.07244	0.536220	+	0.844078i	$0.319852\pi$
$192$	−64.0500	−4.62241
$193$	20.4368	1.47107	0.735536	−	0.677486i	$-0.236931\pi$
$193$	20.4368	1.47107	0.735536	+	0.677486i	$0.236931\pi$
$194$	7.02230	0.504172
$195$	−3.05821	−0.219003
$196$	−15.5574	−1.11124
$197$	15.7689	1.12349	0.561746	−	0.827310i	$-0.310130\pi$
$197$	15.7689	1.12349	0.561746	+	0.827310i	$0.310130\pi$
$198$	22.1142	1.57159
$199$	−23.9848	−1.70023	−0.850117	−	0.526593i	$-0.823469\pi$
$199$	−23.9848	−1.70023	−0.850117	+	0.526593i	$0.823469\pi$
$200$	−2.99287	−0.211628
$201$	12.2134	0.861469
$202$	18.1466	1.27679
$203$	−7.81045	−0.548186
$204$	51.9223	3.63529
$205$	11.3289	0.791244
$206$	−27.0414	−1.88406
$207$	0.0320210	0.00222561
$208$	−18.5599	−1.28690
$209$	−4.81334	−0.332946
$210$	17.8596	1.23243
$211$	26.1839	1.80257	0.901286	−	0.433225i	$-0.142624\pi$
$211$	26.1839	1.80257	0.901286	+	0.433225i	$0.142624\pi$
$212$	−15.0276	−1.03210
$213$	5.96302	0.408579
$214$	2.77155	0.189459
$215$	−12.8758	−0.878122
$216$	−60.7868	−4.13602
$217$	2.29484	0.155784
$218$	−27.4308	−1.85785
$219$	−17.6739	−1.19429
$220$	−86.4330	−5.82731
$221$	6.66259	0.448174
$222$	16.7742	1.12581
$223$	−5.76231	−0.385873	−0.192936	−	0.981211i	$-0.561801\pi$
$223$	−5.76231	−0.385873	−0.192936	+	0.981211i	$0.561801\pi$
$224$	63.3755	4.23445
$225$	−0.340206	−0.0226804
$226$	−36.0967	−2.40112
$227$	−25.4989	−1.69242	−0.846212	−	0.532847i	$-0.821122\pi$
$227$	−25.4989	−1.69242	−0.846212	+	0.532847i	$0.821122\pi$
$228$	5.83604	0.386501
$229$	−1.86995	−0.123570	−0.0617849	−	0.998089i	$-0.519679\pi$
$229$	−1.86995	−0.123570	−0.0617849	+	0.998089i	$0.519679\pi$
$230$	−0.167913	−0.0110718
$231$	17.8309	1.17318
$232$	−40.4808	−2.65770
$233$	−13.4671	−0.882261	−0.441130	−	0.897443i	$-0.645422\pi$
$233$	−13.4671	−0.882261	−0.441130	+	0.897443i	$0.645422\pi$
$234$	−3.44058	−0.224918
$235$	7.98077	0.520608
$236$	−20.5548	−1.33800
$237$	−7.56041	−0.491101
$238$	−38.9088	−2.52208
$239$	−1.65409	−0.106994	−0.0534972	−	0.998568i	$-0.517037\pi$
$239$	−1.65409	−0.106994	−0.0534972	+	0.998568i	$0.517037\pi$
$240$	56.7600	3.66384
$241$	12.0584	0.776750	0.388375	−	0.921501i	$-0.373037\pi$
$241$	12.0584	0.776750	0.388375	+	0.921501i	$0.373037\pi$
$242$	−84.9495	−5.46076
$243$	−11.8130	−0.757803
$244$	−29.5522	−1.89189
$245$	6.10511	0.390041
$246$	−18.3993	−1.17309
$247$	0.748871	0.0476495
$248$	11.8940	0.755267
$249$	6.73170	0.426604
$250$	−30.4052	−1.92299
$251$	25.0065	1.57839	0.789197	−	0.614141i	$-0.210497\pi$
$251$	25.0065	1.57839	0.789197	+	0.614141i	$0.210497\pi$
$252$	14.9760	0.943398
$253$	−0.167643	−0.0105396
$254$	−23.0008	−1.44320
$255$	−20.3756	−1.27597
$256$	111.175	6.94847
$257$	12.1082	0.755287	0.377643	−	0.925951i	$-0.376735\pi$
$257$	12.1082	0.755287	0.377643	+	0.925951i	$0.376735\pi$
$258$	20.9116	1.30190
$259$	−9.36903	−0.582163
$260$	13.4474	0.833975
$261$	−4.60154	−0.284828
$262$	−38.1287	−2.35560
$263$	24.7108	1.52374	0.761868	−	0.647732i	$-0.224283\pi$
$263$	24.7108	1.52374	0.761868	+	0.647732i	$0.224283\pi$
$264$	92.4157	5.68779
$265$	5.89719	0.362261
$266$	−4.37332	−0.268145
$267$	−7.67584	−0.469754
$268$	−53.7044	−3.28052
$269$	−0.408188	−0.0248877	−0.0124438	−	0.999923i	$-0.503961\pi$
$269$	−0.408188	−0.0248877	−0.0124438	+	0.999923i	$0.503961\pi$
$270$	36.2337	2.20511
$271$	−1.78415	−0.108380	−0.0541898	−	0.998531i	$-0.517258\pi$
$271$	−1.78415	−0.108380	−0.0541898	+	0.998531i	$0.517258\pi$
$272$	−123.657	−7.49780
$273$	−2.77417	−0.167900
$274$	20.6475	1.24736
$275$	1.78111	0.107405
$276$	0.203262	0.0122349
$277$	5.88899	0.353835	0.176918	−	0.984226i	$-0.443387\pi$
$277$	5.88899	0.353835	0.176918	+	0.984226i	$0.443387\pi$
$278$	18.1069	1.08598
$279$	1.35201	0.0809427
$280$	−51.7008	−3.08972
$281$	9.67924	0.577415	0.288707	−	0.957417i	$-0.406774\pi$
$281$	9.67924	0.577415	0.288707	+	0.957417i	$0.406774\pi$
$282$	−12.9616	−0.771850
$283$	27.1037	1.61115	0.805573	−	0.592496i	$-0.201857\pi$
$283$	27.1037	1.61115	0.805573	+	0.592496i	$0.201857\pi$
$284$	−26.2204	−1.55589
$285$	−2.29020	−0.135660
$286$	18.0128	1.06512
$287$	10.2767	0.606613
$288$	37.3378	2.20015
$289$	27.3901	1.61118
$290$	24.1297	1.41695
$291$	3.33586	0.195551
$292$	77.7150	4.54792
$293$	−25.4028	−1.48405	−0.742023	−	0.670375i	$-0.766133\pi$
$293$	−25.4028	−1.48405	−0.742023	+	0.670375i	$0.766133\pi$
$294$	−9.91531	−0.578273
$295$	8.06619	0.469632
$296$	−48.5588	−2.82242
$297$	36.1754	2.09911
$298$	24.3809	1.41235
$299$	0.0260822	0.00150837
$300$	−2.15955	−0.124682
$301$	−11.6799	−0.673218
$302$	−4.42303	−0.254517
$303$	8.62032	0.495225
$304$	−13.8989	−0.797159
$305$	11.5970	0.664044
$306$	−22.9232	−1.31043
$307$	3.15115	0.179845	0.0899227	−	0.995949i	$-0.471338\pi$
$307$	3.15115	0.179845	0.0899227	+	0.995949i	$0.471338\pi$
$308$	−78.4052	−4.46755
$309$	−12.8457	−0.730765
$310$	−7.08972	−0.402669
$311$	−14.6078	−0.828334	−0.414167	−	0.910201i	$-0.635927\pi$
$311$	−14.6078	−0.828334	−0.414167	+	0.910201i	$0.635927\pi$
$312$	−14.3782	−0.814007
$313$	−11.7753	−0.665580	−0.332790	−	0.943001i	$-0.607990\pi$
$313$	−11.7753	−0.665580	−0.332790	+	0.943001i	$0.607990\pi$
$314$	−30.3255	−1.71137
$315$	−5.87694	−0.331128
$316$	33.2443	1.87014
$317$	−5.28990	−0.297111	−0.148555	−	0.988904i	$-0.547462\pi$
$317$	−5.28990	−0.297111	−0.148555	+	0.988904i	$0.547462\pi$
$318$	−9.57762	−0.537086
$319$	24.0909	1.34883
$320$	−110.522	−6.17835
$321$	1.31659	0.0734849
$322$	−0.152317	−0.00848830
$323$	4.98942	0.277619
$324$	−22.3013	−1.23896
$325$	−0.277110	−0.0153713
$326$	53.1672	2.94466
$327$	−13.0306	−0.720597
$328$	53.2630	2.94096
$329$	7.23952	0.399128
$330$	−55.0869	−3.03244
$331$	0.0377636	0.00207568	0.00103784	−	0.999999i	$-0.499670\pi$
$331$	0.0377636	0.00207568	0.00103784	+	0.999999i	$0.499670\pi$
$332$	−29.6004	−1.62453
$333$	−5.51978	−0.302482
$334$	49.3255	2.69897
$335$	21.0749	1.15145
$336$	51.4882	2.80891
$337$	30.5643	1.66494	0.832470	−	0.554069i	$-0.186926\pi$
$337$	30.5643	1.66494	0.832470	+	0.554069i	$0.186926\pi$
$338$	−2.80247	−0.152434
$339$	−17.1473	−0.931313
$340$	89.5948	4.85896
$341$	−7.07831	−0.383312
$342$	−2.57655	−0.139324
$343$	20.1249	1.08664
$344$	−60.5358	−3.26387
$345$	−0.0797649	−0.00429440
$346$	14.5157	0.780369
$347$	23.8995	1.28299	0.641497	−	0.767126i	$-0.278314\pi$
$347$	23.8995	1.28299	0.641497	+	0.767126i	$0.278314\pi$
$348$	−29.2095	−1.56579
$349$	−15.3782	−0.823174	−0.411587	−	0.911370i	$-0.635025\pi$
$349$	−15.3782	−0.823174	−0.411587	+	0.911370i	$0.635025\pi$
$350$	1.61829	0.0865012
$351$	−5.62824	−0.300413
$352$	−195.478	−10.4190
$353$	26.5627	1.41379	0.706894	−	0.707320i	$-0.250096\pi$
$353$	26.5627	1.41379	0.706894	+	0.707320i	$0.250096\pi$
$354$	−13.1003	−0.696273
$355$	10.2895	0.546111
$356$	33.7519	1.78885
$357$	−18.4831	−0.978231
$358$	46.7521	2.47092
$359$	29.3161	1.54724	0.773622	−	0.633648i	$-0.218443\pi$
$359$	29.3161	1.54724	0.773622	+	0.633648i	$0.218443\pi$
$360$	−30.4596	−1.60536
$361$	−18.4392	−0.970484
$362$	−55.0286	−2.89224
$363$	−40.3542	−2.11805
$364$	12.1985	0.639373
$365$	−30.4973	−1.59630
$366$	−18.8347	−0.984507
$367$	5.63138	0.293955	0.146978	−	0.989140i	$-0.453045\pi$
$367$	5.63138	0.293955	0.146978	+	0.989140i	$0.453045\pi$
$368$	−0.484083	−0.0252346
$369$	6.05452	0.315186
$370$	28.9448	1.50477
$371$	5.34946	0.277730
$372$	8.58224	0.444969
$373$	−12.2381	−0.633667	−0.316833	−	0.948481i	$-0.602620\pi$
$373$	−12.2381	−0.633667	−0.316833	+	0.948481i	$0.602620\pi$
$374$	120.012	6.20567
$375$	−14.4436	−0.745864
$376$	37.5217	1.93504
$377$	−3.74812	−0.193038
$378$	32.8683	1.69056
$379$	−21.1007	−1.08387	−0.541936	−	0.840420i	$-0.682309\pi$
$379$	−21.1007	−1.08387	−0.541936	+	0.840420i	$0.682309\pi$
$380$	10.0704	0.516601
$381$	−10.9263	−0.559769
$382$	−41.5366	−2.12520
$383$	−19.7449	−1.00892	−0.504458	−	0.863436i	$-0.668308\pi$
$383$	−19.7449	−1.00892	−0.504458	+	0.863436i	$0.668308\pi$
$384$	98.5221	5.02769
$385$	30.7681	1.56809
$386$	−57.2735	−2.91514
$387$	−6.88123	−0.349793
$388$	−14.6683	−0.744670
$389$	−28.7719	−1.45879	−0.729397	−	0.684091i	$-0.760199\pi$
$389$	−28.7719	−1.45879	−0.729397	+	0.684091i	$0.760199\pi$
$390$	8.57055	0.433987
$391$	0.173775	0.00878819
$392$	28.7033	1.44974
$393$	−18.1126	−0.913659
$394$	−44.1920	−2.22636
$395$	−13.0459	−0.656411
$396$	−46.1925	−2.32126
$397$	20.4675	1.02723	0.513617	−	0.858020i	$-0.328305\pi$
$397$	20.4675	1.02723	0.513617	+	0.858020i	$0.328305\pi$
$398$	67.2166	3.36927
$399$	−2.07749	−0.104005
$400$	5.14312	0.257156
$401$	−13.9626	−0.697261	−0.348630	−	0.937260i	$-0.613353\pi$
$401$	−13.9626	−0.697261	−0.348630	+	0.937260i	$0.613353\pi$
$402$	−34.2278	−1.70713
$403$	1.10126	0.0548577
$404$	−37.9050	−1.88584
$405$	8.75159	0.434870
$406$	21.8886	1.08631
$407$	28.8982	1.43243
$408$	−95.7963	−4.74262
$409$	10.2041	0.504561	0.252281	−	0.967654i	$-0.418819\pi$
$409$	10.2041	0.504561	0.252281	+	0.967654i	$0.418819\pi$
$410$	−31.7489	−1.56797
$411$	9.80832	0.483809
$412$	56.4845	2.78279
$413$	7.31701	0.360046
$414$	−0.0897379	−0.00441038
$415$	11.6159	0.570203
$416$	30.4129	1.49112
$417$	8.60148	0.421216
$418$	13.4893	0.659781
$419$	−1.72732	−0.0843851	−0.0421925	−	0.999109i	$-0.513434\pi$
$419$	−1.72732	−0.0843851	−0.0421925	+	0.999109i	$0.513434\pi$
$420$	−37.3054	−1.82032
$421$	−0.687618	−0.0335124	−0.0167562	−	0.999860i	$-0.505334\pi$
$421$	−0.687618	−0.0335124	−0.0167562	+	0.999860i	$0.505334\pi$
$422$	−73.3796	−3.57206
$423$	4.26518	0.207380
$424$	27.7257	1.34648
$425$	−1.84627	−0.0895572
$426$	−16.7112	−0.809660
$427$	10.5199	0.509094
$428$	−5.78926	−0.279835
$429$	8.55676	0.413124
$430$	36.0841	1.74013
$431$	12.1146	0.583538	0.291769	−	0.956489i	$-0.405756\pi$
$431$	12.1146	0.583538	0.291769	+	0.956489i	$0.405756\pi$
$432$	104.459	5.02581
$433$	40.0157	1.92303	0.961516	−	0.274750i	$-0.0885952\pi$
$433$	40.0157	1.92303	0.961516	+	0.274750i	$0.0885952\pi$
$434$	−6.43123	−0.308709
$435$	11.4625	0.549586
$436$	57.2979	2.74407
$437$	0.0195322	0.000934352 0
$438$	49.5306	2.36666
$439$	−7.11638	−0.339646	−0.169823	−	0.985475i	$-0.554320\pi$
$439$	−7.11638	−0.339646	−0.169823	+	0.985475i	$0.554320\pi$
$440$	159.468	7.60235
$441$	3.26277	0.155370
$442$	−18.6717	−0.888123
$443$	27.5017	1.30664	0.653322	−	0.757080i	$-0.273375\pi$
$443$	27.5017	1.30664	0.653322	+	0.757080i	$0.273375\pi$
$444$	−35.0383	−1.66284
$445$	−13.2451	−0.627877
$446$	16.1487	0.764664
$447$	11.5818	0.547802
$448$	−100.257	−4.73668
$449$	−34.8290	−1.64368	−0.821842	−	0.569716i	$-0.807053\pi$
$449$	−34.8290	−1.64368	−0.821842	+	0.569716i	$0.807053\pi$
$450$	0.953418	0.0449445
$451$	−31.6978	−1.49259
$452$	75.3994	3.54649
$453$	−2.10111	−0.0987186
$454$	71.4601	3.35379
$455$	−4.78697	−0.224417
$456$	−10.7674	−0.504232
$457$	−24.5379	−1.14783	−0.573917	−	0.818914i	$-0.694577\pi$
$457$	−24.5379	−1.14783	−0.573917	+	0.818914i	$0.694577\pi$
$458$	5.24048	0.244872
$459$	−37.4987	−1.75029
$460$	0.350739	0.0163533
$461$	32.4700	1.51228	0.756139	−	0.654411i	$-0.227083\pi$
$461$	32.4700	1.51228	0.756139	+	0.654411i	$0.227083\pi$
$462$	−49.9705	−2.32484
$463$	21.3301	0.991292	0.495646	−	0.868524i	$-0.334931\pi$
$463$	21.3301	0.991292	0.495646	+	0.868524i	$0.334931\pi$
$464$	69.5646	3.22945
$465$	−3.36788	−0.156182
$466$	37.7413	1.74833
$467$	−19.6519	−0.909383	−0.454691	−	0.890649i	$-0.650250\pi$
$467$	−19.6519	−0.909383	−0.454691	+	0.890649i	$0.650250\pi$
$468$	7.18674	0.332207
$469$	19.1175	0.882765
$470$	−22.3659	−1.03166
$471$	−14.4058	−0.663783
$472$	37.9234	1.74556
$473$	36.0260	1.65648
$474$	21.1878	0.973190
$475$	−0.207519	−0.00952164
$476$	81.2733	3.72516
$477$	3.15164	0.144304
$478$	4.63555	0.212025
$479$	34.2666	1.56568	0.782840	−	0.622223i	$-0.213770\pi$
$479$	34.2666	1.56568	0.782840	+	0.622223i	$0.213770\pi$
$480$	−93.0091	−4.24526
$481$	−4.49605	−0.205002
$482$	−33.7933	−1.53924
$483$	−0.0723564	−0.00329233
$484$	177.444	8.06563
$485$	5.75621	0.261376
$486$	33.1055	1.50170
$487$	−11.4437	−0.518565	−0.259282	−	0.965802i	$-0.583486\pi$
$487$	−11.4437	−0.518565	−0.259282	+	0.965802i	$0.583486\pi$
$488$	54.5237	2.46817
$489$	25.2564	1.14213
$490$	−17.1094	−0.772924
$491$	−18.1168	−0.817601	−0.408801	−	0.912624i	$-0.634053\pi$
$491$	−18.1168	−0.817601	−0.408801	+	0.912624i	$0.634053\pi$
$492$	38.4327	1.73268
$493$	−24.9722	−1.12469
$494$	−2.09869	−0.0944245
$495$	18.1271	0.814752
$496$	−20.4392	−0.917749
$497$	9.33383	0.418679
$498$	−18.8654	−0.845378
$499$	27.0252	1.20981	0.604906	−	0.796297i	$-0.293211\pi$
$499$	27.0252	1.20981	0.604906	+	0.796297i	$0.293211\pi$
$500$	63.5108	2.84029
$501$	23.4315	1.04684
$502$	−70.0799	−3.12782
$503$	−14.4053	−0.642301	−0.321150	−	0.947028i	$-0.604070\pi$
$503$	−14.4053	−0.642301	−0.321150	+	0.947028i	$0.604070\pi$
$504$	−27.6306	−1.23076
$505$	14.8748	0.661922
$506$	0.469814	0.0208858
$507$	−1.33128	−0.0591242
$508$	48.0445	2.13163
$509$	32.7142	1.45003	0.725015	−	0.688733i	$-0.241833\pi$
$509$	32.7142	1.45003	0.725015	+	0.688733i	$0.241833\pi$
$510$	57.1021	2.52852
$511$	−27.6647	−1.22381
$512$	−163.555	−7.22818
$513$	−4.21483	−0.186089
$514$	−33.9328	−1.49671
$515$	−22.1659	−0.976747
$516$	−43.6804	−1.92292
$517$	−22.3299	−0.982067
$518$	26.2564	1.15364
$519$	6.89551	0.302679
$520$	−24.8104	−1.08801
$521$	7.61479	0.333610	0.166805	−	0.985990i	$-0.446655\pi$
$521$	7.61479	0.333610	0.166805	+	0.985990i	$0.446655\pi$
$522$	12.8957	0.564429
$523$	−40.0288	−1.75034	−0.875168	−	0.483819i	$-0.839249\pi$
$523$	−40.0288	−1.75034	−0.875168	+	0.483819i	$0.839249\pi$
$524$	79.6439	3.47926
$525$	0.768748	0.0335509
$526$	−69.2515	−3.01951
$527$	7.33724	0.319615
$528$	−158.812	−6.91142
$529$	−22.9993	−0.999970
$530$	−16.5267	−0.717874
$531$	4.31083	0.187074
$532$	9.13507	0.396055
$533$	4.93162	0.213612
$534$	21.5113	0.930886
$535$	2.27185	0.0982206
$536$	99.0842	4.27979
$537$	22.2090	0.958389
$538$	1.14394	0.0493186
$539$	−17.0819	−0.735769
$540$	−75.6855	−3.25699
$541$	−0.716864	−0.0308204	−0.0154102	−	0.999881i	$-0.504905\pi$
$541$	−0.716864	−0.0308204	−0.0154102	+	0.999881i	$0.504905\pi$
$542$	5.00004	0.214770
$543$	−26.1406	−1.12180
$544$	202.629	8.68764
$545$	−22.4851	−0.963156
$546$	7.77452	0.332719
$547$	15.4359	0.659990	0.329995	−	0.943983i	$-0.392953\pi$
$547$	15.4359	0.659990	0.329995	+	0.943983i	$0.392953\pi$
$548$	−43.1288	−1.84237
$549$	6.19782	0.264517
$550$	−4.99152	−0.212839
$551$	−2.80685	−0.119576
$552$	−0.375016	−0.0159618
$553$	−11.8342	−0.503242
$554$	−16.5037	−0.701177
$555$	13.7499	0.583650
$556$	−37.8221	−1.60401
$557$	−3.33044	−0.141115	−0.0705577	−	0.997508i	$-0.522478\pi$
$557$	−3.33044	−0.141115	−0.0705577	+	0.997508i	$0.522478\pi$
$558$	−3.78897	−0.160400
$559$	−5.60500	−0.237066
$560$	88.8456	3.75441
$561$	57.0102	2.40697
$562$	−27.1258	−1.14423
$563$	−12.9806	−0.547066	−0.273533	−	0.961863i	$-0.588192\pi$
$563$	−12.9806	−0.547066	−0.273533	+	0.961863i	$0.588192\pi$
$564$	27.0743	1.14003
$565$	−29.5886	−1.24480
$566$	−75.9573	−3.19272
$567$	7.93875	0.333396
$568$	48.3764	2.02983
$569$	−21.8981	−0.918014	−0.459007	−	0.888433i	$-0.651795\pi$
$569$	−21.8981	−0.918014	−0.459007	+	0.888433i	$0.651795\pi$
$570$	6.41824	0.268830
$571$	33.6877	1.40979	0.704893	−	0.709314i	$-0.250995\pi$
$571$	33.6877	1.40979	0.704893	+	0.709314i	$0.250995\pi$
$572$	−37.6254	−1.57320
$573$	−19.7315	−0.824294
$574$	−28.8001	−1.20209
$575$	−0.00722763	−0.000301413 0
$576$	−59.0663	−2.46110
$577$	−22.6095	−0.941244	−0.470622	−	0.882335i	$-0.655970\pi$
$577$	−22.6095	−0.941244	−0.470622	+	0.882335i	$0.655970\pi$
$578$	−76.7601	−3.19280
$579$	−27.2071	−1.13069
$580$	−50.4026	−2.09285
$581$	10.5370	0.437150
$582$	−9.34865	−0.387514
$583$	−16.5001	−0.683365
$584$	−143.384	−5.93325
$585$	−2.82025	−0.116603
$586$	71.1905	2.94085
$587$	−33.2622	−1.37288	−0.686439	−	0.727188i	$-0.740827\pi$
$587$	−33.2622	−1.37288	−0.686439	+	0.727188i	$0.740827\pi$
$588$	20.7113	0.854118
$589$	0.824701	0.0339812
$590$	−22.6053	−0.930645
$591$	−20.9929	−0.863532
$592$	83.4462	3.42962
$593$	−21.9647	−0.901981	−0.450990	−	0.892529i	$-0.648929\pi$
$593$	−21.9647	−0.901981	−0.450990	+	0.892529i	$0.648929\pi$
$594$	−101.380	−4.15969
$595$	−31.8937	−1.30751
$596$	−50.9272	−2.08606
$597$	31.9304	1.30683
$598$	−0.0730947	−0.00298906
$599$	36.0011	1.47097	0.735483	−	0.677543i	$-0.236955\pi$
$599$	36.0011	1.47097	0.735483	+	0.677543i	$0.236955\pi$
$600$	3.98435	0.162660
$601$	26.4229	1.07781	0.538905	−	0.842366i	$-0.318838\pi$
$601$	26.4229	1.07781	0.538905	+	0.842366i	$0.318838\pi$
$602$	32.7326	1.33408
$603$	11.2631	0.458669
$604$	9.23890	0.375926
$605$	−69.6334	−2.83100
$606$	−24.1582	−0.981361
$607$	−9.27802	−0.376583	−0.188292	−	0.982113i	$-0.560295\pi$
$607$	−9.27802	−0.376583	−0.188292	+	0.982113i	$0.560295\pi$
$608$	22.7753	0.923662
$609$	10.3979	0.421344
$610$	−32.5004	−1.31590
$611$	3.47413	0.140548
$612$	47.8823	1.93553
$613$	33.8453	1.36700	0.683500	−	0.729950i	$-0.260457\pi$
$613$	33.8453	1.36700	0.683500	+	0.729950i	$0.260457\pi$
$614$	−8.83100	−0.356390
$615$	−15.0819	−0.608162
$616$	144.657	5.82839
$617$	−39.5823	−1.59352	−0.796762	−	0.604294i	$-0.793455\pi$
$617$	−39.5823	−1.59352	−0.796762	+	0.604294i	$0.793455\pi$
$618$	35.9997	1.44812
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	14.8091	0.594749
$621$	−0.146797	−0.00589076
$622$	40.9381	1.64147
$623$	−12.0149	−0.481366
$624$	24.7084	0.989127
$625$	−26.3088	−1.05235
$626$	33.0000	1.31894
$627$	6.40791	0.255907
$628$	63.3445	2.52772
$629$	−29.9554	−1.19440
$630$	16.4700	0.656179
$631$	−24.3693	−0.970125	−0.485063	−	0.874479i	$-0.661203\pi$
$631$	−24.3693	−0.970125	−0.485063	+	0.874479i	$0.661203\pi$
$632$	−61.3356	−2.43980
$633$	−34.8580	−1.38548
$634$	14.8248	0.588768
$635$	−18.8539	−0.748193
$636$	20.0059	0.793285
$637$	2.65764	0.105299
$638$	−67.5141	−2.67291
$639$	5.49904	0.217539
$640$	170.005	6.72005
$641$	8.36873	0.330545	0.165273	−	0.986248i	$-0.447150\pi$
$641$	8.36873	0.330545	0.165273	+	0.986248i	$0.447150\pi$
$642$	−3.68971	−0.145621
$643$	−39.0540	−1.54014	−0.770069	−	0.637961i	$-0.779778\pi$
$643$	−39.0540	−1.54014	−0.770069	+	0.637961i	$0.779778\pi$
$644$	0.318163	0.0125374
$645$	17.1413	0.674937
$646$	−13.9827	−0.550142
$647$	21.1252	0.830517	0.415259	−	0.909703i	$-0.363691\pi$
$647$	21.1252	0.830517	0.415259	+	0.909703i	$0.363691\pi$
$648$	41.1458	1.61636
$649$	−22.5689	−0.885907
$650$	0.776592	0.0304605
$651$	−3.05508	−0.119738
$652$	−111.057	−4.34931
$653$	−5.12344	−0.200496	−0.100248	−	0.994962i	$-0.531964\pi$
$653$	−5.12344	−0.200496	−0.100248	+	0.994962i	$0.531964\pi$
$654$	36.5180	1.42797
$655$	−31.2542	−1.22120
$656$	−91.5302	−3.57366
$657$	−16.2987	−0.635873
$658$	−20.2886	−0.790930
$659$	−11.4976	−0.447884	−0.223942	−	0.974602i	$-0.571893\pi$
$659$	−11.4976	−0.447884	−0.223942	+	0.974602i	$0.571893\pi$
$660$	115.067	4.47896
$661$	−6.83738	−0.265943	−0.132972	−	0.991120i	$-0.542452\pi$
$661$	−6.83738	−0.265943	−0.132972	+	0.991120i	$0.542452\pi$
$662$	−0.105831	−0.00411326
$663$	−8.86977	−0.344473
$664$	54.6124	2.11937
$665$	−3.58483	−0.139014
$666$	15.4690	0.599413
$667$	−0.0977592	−0.00378525
$668$	−103.032	−3.98643
$669$	7.67125	0.296587
$670$	−59.0619	−2.28176
$671$	−32.4481	−1.25264
$672$	−84.3705	−3.25466
$673$	−22.0010	−0.848077	−0.424039	−	0.905644i	$-0.639388\pi$
$673$	−22.0010	−0.848077	−0.424039	+	0.905644i	$0.639388\pi$
$674$	−85.6555	−3.29933
$675$	1.55964	0.0600306
$676$	5.85385	0.225148
$677$	29.2963	1.12595	0.562974	−	0.826475i	$-0.309657\pi$
$677$	29.2963	1.12595	0.562974	+	0.826475i	$0.309657\pi$
$678$	48.0548	1.84553
$679$	5.22157	0.200386
$680$	−165.302	−6.33903
$681$	33.9462	1.30082
$682$	19.8368	0.759589
$683$	−0.614150	−0.0234998	−0.0117499	−	0.999931i	$-0.503740\pi$
$683$	−0.614150	−0.0234998	−0.0117499	+	0.999931i	$0.503740\pi$
$684$	5.38194	0.205784
$685$	16.9248	0.646663
$686$	−56.3995	−2.15334
$687$	2.48943	0.0949775
$688$	104.028	3.96604
$689$	2.56712	0.0977996
$690$	0.223539	0.00850998
$691$	−16.5155	−0.628281	−0.314140	−	0.949377i	$-0.601716\pi$
$691$	−16.5155	−0.628281	−0.314140	+	0.949377i	$0.601716\pi$
$692$	−30.3206	−1.15262
$693$	16.4435	0.624635
$694$	−66.9777	−2.54244
$695$	14.8423	0.563001
$696$	53.8913	2.04274
$697$	32.8574	1.24456
$698$	43.0969	1.63124
$699$	17.9285	0.678119
$700$	−3.38031	−0.127764
$701$	−19.4115	−0.733162	−0.366581	−	0.930386i	$-0.619472\pi$
$701$	−19.4115	−0.733162	−0.366581	+	0.930386i	$0.619472\pi$
$702$	15.7730	0.595313
$703$	−3.36696	−0.126987
$704$	309.236	11.6548
$705$	−10.6246	−0.400147
$706$	−74.4411	−2.80163
$707$	13.4933	0.507467
$708$	27.3641	1.02841
$709$	15.8040	0.593530	0.296765	−	0.954951i	$-0.404092\pi$
$709$	15.8040	0.593530	0.296765	+	0.954951i	$0.404092\pi$
$710$	−28.8361	−1.08220
$711$	−6.97214	−0.261476
$712$	−62.2720	−2.33374
$713$	0.0287233	0.00107570
$714$	51.7985	1.93851
$715$	14.7652	0.552185
$716$	−97.6565	−3.64959
$717$	2.20206	0.0822375
$718$	−82.1575	−3.06609
$719$	29.1824	1.08832	0.544159	−	0.838982i	$-0.316849\pi$
$719$	29.1824	1.08832	0.544159	+	0.838982i	$0.316849\pi$
$720$	52.3436	1.95073
$721$	−20.1072	−0.748830
$722$	51.6753	1.92316
$723$	−16.0531	−0.597021
$724$	114.945	4.27188
$725$	1.03864	0.0385741
$726$	113.092	4.19722
$727$	−31.4866	−1.16777	−0.583886	−	0.811835i	$-0.698469\pi$
$727$	−31.4866	−1.16777	−0.583886	+	0.811835i	$0.698469\pi$
$728$	−22.5061	−0.834130
$729$	27.1554	1.00576
$730$	85.4678	3.16330
$731$	−37.3438	−1.38121
$732$	39.3423	1.45413
$733$	−20.1864	−0.745600	−0.372800	−	0.927912i	$-0.621602\pi$
$733$	−20.1864	−0.745600	−0.372800	+	0.927912i	$0.621602\pi$
$734$	−15.7818	−0.582516
$735$	−8.12761	−0.299792
$736$	0.793236	0.0292391
$737$	−58.9669	−2.17207
$738$	−16.9676	−0.624587
$739$	30.1033	1.10737	0.553684	−	0.832727i	$-0.313221\pi$
$739$	30.1033	1.10737	0.553684	+	0.832727i	$0.313221\pi$
$740$	−60.4604	−2.22257
$741$	−0.996957	−0.0366241
$742$	−14.9917	−0.550363
$743$	−2.39455	−0.0878475	−0.0439237	−	0.999035i	$-0.513986\pi$
$743$	−2.39455	−0.0878475	−0.0439237	+	0.999035i	$0.513986\pi$
$744$	−15.8342	−0.580509
$745$	19.9851	0.732197
$746$	34.2970	1.25570
$747$	6.20791	0.227136
$748$	−250.683	−9.16588
$749$	2.06084	0.0753015
$750$	40.4778	1.47804
$751$	2.64902	0.0966643	0.0483321	−	0.998831i	$-0.484609\pi$
$751$	2.64902	0.0966643	0.0483321	+	0.998831i	$0.484609\pi$
$752$	−64.4795	−2.35133
$753$	−33.2906	−1.21318
$754$	10.5040	0.382533
$755$	−3.62557	−0.131948
$756$	−68.6559	−2.49699
$757$	31.0825	1.12971	0.564857	−	0.825189i	$-0.308931\pi$
$757$	31.0825	1.12971	0.564857	+	0.825189i	$0.308931\pi$
$758$	59.1342	2.14785
$759$	0.223179	0.00810089
$760$	−18.5798	−0.673961
$761$	−42.7987	−1.55145	−0.775725	−	0.631071i	$-0.782616\pi$
$761$	−42.7987	−1.55145	−0.775725	+	0.631071i	$0.782616\pi$
$762$	30.6205	1.10927
$763$	−20.3967	−0.738410
$764$	86.7624	3.13895
$765$	−18.7902	−0.679361
$766$	55.3344	1.99931
$767$	3.51132	0.126786
$768$	−148.006	−5.34069
$769$	7.05066	0.254253	0.127127	−	0.991886i	$-0.459425\pi$
$769$	7.05066	0.254253	0.127127	+	0.991886i	$0.459425\pi$
$770$	−86.2268	−3.10740
$771$	−16.1194	−0.580525
$772$	119.634	4.30572
$773$	33.1458	1.19217	0.596086	−	0.802920i	$-0.296722\pi$
$773$	33.1458	1.19217	0.596086	+	0.802920i	$0.296722\pi$
$774$	19.2845	0.693166
$775$	−0.305170	−0.0109620
$776$	27.0629	0.971502
$777$	12.4728	0.447459
$778$	80.6325	2.89082
$779$	3.69315	0.132321
$780$	−17.9023	−0.641006
$781$	−28.7897	−1.03018
$782$	−0.487000	−0.0174151
$783$	21.0953	0.753885
$784$	−49.3254	−1.76162
$785$	−24.8579	−0.887218
$786$	50.7600	1.81055
$787$	−42.8131	−1.52612	−0.763062	−	0.646326i	$-0.776305\pi$
$787$	−42.8131	−1.52612	−0.763062	+	0.646326i	$0.776305\pi$
$788$	92.3091	3.28837
$789$	−32.8970	−1.17117
$790$	36.5608	1.30077
$791$	−26.8404	−0.954335
$792$	85.2249	3.02833
$793$	5.04834	0.179272
$794$	−57.3596	−2.03562
$795$	−7.85080	−0.278439
$796$	−140.403	−4.97646
$797$	−45.6926	−1.61851	−0.809257	−	0.587454i	$-0.800130\pi$
$797$	−45.6926	−1.61851	−0.809257	+	0.587454i	$0.800130\pi$
$798$	5.82211	0.206101
$799$	23.1467	0.818873
$800$	−8.42771	−0.297965
$801$	−7.07859	−0.250110
$802$	39.1299	1.38173
$803$	85.3302	3.01124
$804$	71.4956	2.52146
$805$	−0.124855	−0.00440056
$806$	−3.08625	−0.108709
$807$	0.543412	0.0191290
$808$	69.9344	2.46028
$809$	−23.4648	−0.824979	−0.412490	−	0.910962i	$-0.635341\pi$
$809$	−23.4648	−0.824979	−0.412490	+	0.910962i	$0.635341\pi$
$810$	−24.5261	−0.861759
$811$	−18.5505	−0.651395	−0.325698	−	0.945474i	$-0.605599\pi$
$811$	−18.5505	−0.651395	−0.325698	+	0.945474i	$0.605599\pi$
$812$	−45.7212	−1.60450
$813$	2.37521	0.0833022
$814$	−80.9865	−2.83858
$815$	43.5813	1.52659
$816$	164.622	5.76292
$817$	−4.19742	−0.146849
$818$	−28.5968	−0.999862
$819$	−2.55831	−0.0893946
$820$	66.3177	2.31591
$821$	−47.4921	−1.65748	−0.828742	−	0.559631i	$-0.810943\pi$
$821$	−47.4921	−1.65748	−0.828742	+	0.559631i	$0.810943\pi$
$822$	−27.4876	−0.958738
$823$	1.37448	0.0479115	0.0239557	−	0.999713i	$-0.492374\pi$
$823$	1.37448	0.0479115	0.0239557	+	0.999713i	$0.492374\pi$
$824$	−104.214	−3.63045
$825$	−2.37116	−0.0825532
$826$	−20.5057	−0.713485
$827$	15.6909	0.545625	0.272813	−	0.962067i	$-0.412046\pi$
$827$	15.6909	0.545625	0.272813	+	0.962067i	$0.412046\pi$
$828$	0.187446	0.00651420
$829$	−56.9633	−1.97842	−0.989208	−	0.146518i	$-0.953193\pi$
$829$	−56.9633	−1.97842	−0.989208	+	0.146518i	$0.953193\pi$
$830$	−32.5533	−1.12994
$831$	−7.83990	−0.271963
$832$	−48.1116	−1.66797
$833$	17.7067	0.613502
$834$	−24.1054	−0.834702
$835$	40.4323	1.39922
$836$	−28.1766	−0.974508
$837$	−6.19816	−0.214240
$838$	4.84077	0.167221
$839$	15.8334	0.546631	0.273315	−	0.961925i	$-0.411880\pi$
$839$	15.8334	0.546631	0.273315	+	0.961925i	$0.411880\pi$
$840$	68.8283	2.37480
$841$	−14.9516	−0.515573
$842$	1.92703	0.0664098
$843$	−12.8858	−0.443810
$844$	153.276	5.27599
$845$	−2.29720	−0.0790259
$846$	−11.9530	−0.410954
$847$	−63.1659	−2.17041
$848$	−47.6455	−1.63615
$849$	−36.0826	−1.23835
$850$	5.17412	0.177471
$851$	−0.117267	−0.00401986
$852$	34.9066	1.19588
$853$	56.5374	1.93580	0.967902	−	0.251328i	$-0.0808672\pi$
$853$	56.5374	1.93580	0.967902	+	0.251328i	$0.0808672\pi$
$854$	−29.4817	−1.00884
$855$	−2.11201	−0.0722291
$856$	10.6811	0.365074
$857$	27.9155	0.953576	0.476788	−	0.879018i	$-0.341801\pi$
$857$	27.9155	0.953576	0.476788	+	0.879018i	$0.341801\pi$
$858$	−23.9801	−0.818666
$859$	−42.4812	−1.44944	−0.724720	−	0.689044i	$-0.758031\pi$
$859$	−42.4812	−1.44944	−0.724720	+	0.689044i	$0.758031\pi$
$860$	−75.3730	−2.57020
$861$	−13.6811	−0.466252
$862$	−33.9507	−1.15637
$863$	−30.4567	−1.03676	−0.518379	−	0.855151i	$-0.673465\pi$
$863$	−30.4567	−1.03676	−0.518379	+	0.855151i	$0.673465\pi$
$864$	−171.171	−5.82337
$865$	11.8986	0.404564
$866$	−112.143	−3.81077
$867$	−36.4639	−1.23838
$868$	13.4337	0.455968
$869$	36.5019	1.23824
$870$	−32.1234	−1.08909
$871$	9.17420	0.310856
$872$	−105.714	−3.57993
$873$	3.07630	0.104117
$874$	−0.0547385	−0.00185156
$875$	−22.6084	−0.764302
$876$	−103.460	−3.49560
$877$	−42.4480	−1.43337	−0.716683	−	0.697399i	$-0.754341\pi$
$877$	−42.4480	−1.43337	−0.716683	+	0.697399i	$0.754341\pi$
$878$	19.9435	0.673059
$879$	33.8182	1.14066
$880$	−274.039	−9.23787
$881$	8.68866	0.292728	0.146364	−	0.989231i	$-0.453243\pi$
$881$	8.68866	0.292728	0.146364	+	0.989231i	$0.453243\pi$
$882$	−9.14381	−0.307888
$883$	4.70900	0.158470	0.0792352	−	0.996856i	$-0.474752\pi$
$883$	4.70900	0.158470	0.0792352	+	0.996856i	$0.474752\pi$
$884$	39.0018	1.31177
$885$	−10.7384	−0.360966
$886$	−77.0727	−2.58931
$887$	28.3339	0.951358	0.475679	−	0.879619i	$-0.342202\pi$
$887$	28.3339	0.951358	0.475679	+	0.879619i	$0.342202\pi$
$888$	64.6453	2.16936
$889$	−17.1027	−0.573607
$890$	37.1190	1.24423
$891$	−24.4866	−0.820333
$892$	−33.7317	−1.12942
$893$	2.60168	0.0870618
$894$	−32.4578	−1.08555
$895$	38.3228	1.28099
$896$	154.215	5.15197
$897$	−0.0347227	−0.00115936
$898$	97.6074	3.25720
$899$	−4.12765	−0.137665
$900$	−1.99152	−0.0663838
$901$	17.1037	0.569807
$902$	88.8323	2.95779
$903$	15.5492	0.517445
$904$	−139.111	−4.62677
$905$	−45.1071	−1.49941
$906$	5.88829	0.195625
$907$	1.89115	0.0627946	0.0313973	−	0.999507i	$-0.490004\pi$
$907$	1.89115	0.0627946	0.0313973	+	0.999507i	$0.490004\pi$
$908$	−149.267	−4.95360
$909$	7.94959	0.263671
$910$	13.4154	0.444715
$911$	−23.5849	−0.781402	−0.390701	−	0.920518i	$-0.627767\pi$
$911$	−23.5849	−0.781402	−0.390701	+	0.920518i	$0.627767\pi$
$912$	18.5034	0.612708
$913$	−32.5009	−1.07562
$914$	68.7667	2.27460
$915$	−15.4389	−0.510394
$916$	−10.9464	−0.361679
$917$	−28.3514	−0.936245
$918$	105.089	3.46845
$919$	−2.36714	−0.0780849	−0.0390424	−	0.999238i	$-0.512431\pi$
$919$	−2.36714	−0.0780849	−0.0390424	+	0.999238i	$0.512431\pi$
$920$	−0.647111	−0.0213346
$921$	−4.19506	−0.138232
$922$	−90.9963	−2.99680
$923$	4.47916	0.147433
$924$	104.379	3.43382
$925$	1.24590	0.0409649
$926$	−59.7769	−1.96439
$927$	−11.8462	−0.389079
$928$	−113.991	−3.74194
$929$	−32.1185	−1.05377	−0.526887	−	0.849935i	$-0.676641\pi$
$929$	−32.1185	−1.05377	−0.526887	+	0.849935i	$0.676641\pi$
$930$	9.43840	0.309497
$931$	1.99023	0.0652271
$932$	−78.8346	−2.58231
$933$	19.4471	0.636670
$934$	55.0740	1.80208
$935$	98.3742	3.21718
$936$	−13.2595	−0.433400
$937$	−34.4879	−1.12667	−0.563336	−	0.826228i	$-0.690482\pi$
$937$	−34.4879	−1.12667	−0.563336	+	0.826228i	$0.690482\pi$
$938$	−53.5763	−1.74933
$939$	15.6762	0.511575
$940$	46.7182	1.52378
$941$	11.3138	0.368820	0.184410	−	0.982849i	$-0.440963\pi$
$941$	11.3138	0.368820	0.184410	+	0.982849i	$0.440963\pi$
$942$	40.3718	1.31538
$943$	0.128628	0.00418869
$944$	−65.1697	−2.12109
$945$	26.9423	0.876432
$946$	−100.962	−3.28255
$947$	26.4068	0.858107	0.429053	−	0.903279i	$-0.358847\pi$
$947$	26.4068	0.858107	0.429053	+	0.903279i	$0.358847\pi$
$948$	−44.2575	−1.43742
$949$	−13.2759	−0.430953
$950$	0.581567	0.0188685
$951$	7.04234	0.228364
$952$	−149.949	−4.85986
$953$	39.4421	1.27766	0.638828	−	0.769350i	$-0.279420\pi$
$953$	39.4421	1.27766	0.638828	+	0.769350i	$0.279420\pi$
$954$	−8.83239	−0.285959
$955$	−34.0477	−1.10176
$956$	−9.68282	−0.313165
$957$	−32.0717	−1.03673
$958$	−96.0312	−3.10263
$959$	15.3528	0.495769
$960$	147.135	4.74877
$961$	−29.7872	−0.960878
$962$	12.6001	0.406242
$963$	1.21415	0.0391254
$964$	70.5881	2.27349
$965$	−46.9473	−1.51129
$966$	0.202777	0.00652424
$967$	−58.2443	−1.87301	−0.936506	−	0.350652i	$-0.885960\pi$
$967$	−58.2443	−1.87301	−0.936506	+	0.350652i	$0.885960\pi$
$968$	−327.383	−10.5225
$969$	−6.64231	−0.213382
$970$	−16.1316	−0.517955
$971$	−2.63586	−0.0845887	−0.0422943	−	0.999105i	$-0.513467\pi$
$971$	−2.63586	−0.0845887	−0.0422943	+	0.999105i	$0.513467\pi$
$972$	−69.1514	−2.21803
$973$	13.4638	0.431629
$974$	32.0707	1.02761
$975$	0.368910	0.0118146
$976$	−93.6966	−2.99915
$977$	28.1923	0.901951	0.450975	−	0.892536i	$-0.351076\pi$
$977$	28.1923	0.901951	0.450975	+	0.892536i	$0.351076\pi$
$978$	−70.7804	−2.26331
$979$	37.0592	1.18442
$980$	35.7384	1.14162
$981$	−12.0167	−0.383665
$982$	50.7719	1.62020
$983$	−31.8909	−1.01716	−0.508580	−	0.861014i	$-0.669830\pi$
$983$	−31.8909	−1.01716	−0.508580	+	0.861014i	$0.669830\pi$
$984$	−70.9080	−2.26046
$985$	−36.2244	−1.15420
$986$	69.9838	2.22874
$987$	−9.63782	−0.306775
$988$	4.38378	0.139467
$989$	−0.146191	−0.00464860
$990$	−50.8007	−1.61455
$991$	−51.1140	−1.62369	−0.811845	−	0.583873i	$-0.801536\pi$
$991$	−51.1140	−1.62369	−0.811845	+	0.583873i	$0.801536\pi$
$992$	33.4925	1.06339
$993$	−0.0502739	−0.00159539
$994$	−26.1578	−0.829675
$995$	55.0977	1.74671
$996$	39.4063	1.24864
$997$	45.9752	1.45605	0.728025	−	0.685550i	$-0.240438\pi$
$997$	45.9752	1.45605	0.728025	+	0.685550i	$0.240438\pi$
$998$	−75.7373	−2.39742
$999$	25.3049	0.800611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.1	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.1	✓	151	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80247 q^{2} -1.33128 q^{3} +5.85385 q^{4} -2.29720 q^{5} +3.73087 q^{6} -2.08383 q^{7} -10.8003 q^{8} -1.22769 q^{9} +O(q^{10})\)	\(q-2.80247 q^{2} -1.33128 q^{3} +5.85385 q^{4} -2.29720 q^{5} +3.73087 q^{6} -2.08383 q^{7} -10.8003 q^{8} -1.22769 q^{9} +6.43783 q^{10} +6.42747 q^{11} -7.79311 q^{12} -1.00000 q^{13} +5.83989 q^{14} +3.05821 q^{15} +18.5599 q^{16} -6.66259 q^{17} +3.44058 q^{18} -0.748871 q^{19} -13.4474 q^{20} +2.77417 q^{21} -18.0128 q^{22} -0.0260822 q^{23} +14.3782 q^{24} +0.277110 q^{25} +2.80247 q^{26} +5.62824 q^{27} -12.1985 q^{28} +3.74812 q^{29} -8.57055 q^{30} -1.10126 q^{31} -30.4129 q^{32} -8.55676 q^{33} +18.6717 q^{34} +4.78697 q^{35} -7.18674 q^{36} +4.49605 q^{37} +2.09869 q^{38} +1.33128 q^{39} +24.8104 q^{40} -4.93162 q^{41} -7.77452 q^{42} +5.60500 q^{43} +37.6254 q^{44} +2.82025 q^{45} +0.0730947 q^{46} -3.47413 q^{47} -24.7084 q^{48} -2.65764 q^{49} -0.776592 q^{50} +8.86977 q^{51} -5.85385 q^{52} -2.56712 q^{53} -15.7730 q^{54} -14.7652 q^{55} +22.5061 q^{56} +0.996957 q^{57} -10.5040 q^{58} -3.51132 q^{59} +17.9023 q^{60} -5.04834 q^{61} +3.08625 q^{62} +2.55831 q^{63} +48.1116 q^{64} +2.29720 q^{65} +23.9801 q^{66} -9.17420 q^{67} -39.0018 q^{68} +0.0347227 q^{69} -13.4154 q^{70} -4.47916 q^{71} +13.2595 q^{72} +13.2759 q^{73} -12.6001 q^{74} -0.368910 q^{75} -4.38378 q^{76} -13.3938 q^{77} -3.73087 q^{78} +5.67905 q^{79} -42.6357 q^{80} -3.80968 q^{81} +13.8207 q^{82} -5.05656 q^{83} +16.2396 q^{84} +15.3053 q^{85} -15.7079 q^{86} -4.98979 q^{87} -69.4187 q^{88} +5.76576 q^{89} -7.90369 q^{90} +2.08383 q^{91} -0.152681 q^{92} +1.46608 q^{93} +9.73617 q^{94} +1.72030 q^{95} +40.4881 q^{96} -2.50575 q^{97} +7.44795 q^{98} -7.89097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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