LMFDB - Embedded newform 8015.2.a.l.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +O(q^{10})$	\(q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +0.348082 q^{10} -2.76949 q^{11} -3.10179 q^{12} -4.02564 q^{13} +0.348082 q^{14} -1.65091 q^{15} +3.28771 q^{16} -1.29135 q^{17} +0.0955480 q^{18} -4.23831 q^{19} +1.87884 q^{20} -1.65091 q^{21} +0.964009 q^{22} +9.13506 q^{23} +2.22898 q^{24} +1.00000 q^{25} +1.40125 q^{26} -5.40590 q^{27} +1.87884 q^{28} -0.484842 q^{29} +0.574652 q^{30} +1.36515 q^{31} -3.84470 q^{32} -4.57218 q^{33} +0.449496 q^{34} +1.00000 q^{35} +0.515739 q^{36} -8.84752 q^{37} +1.47528 q^{38} -6.64597 q^{39} -1.35015 q^{40} -9.64385 q^{41} +0.574652 q^{42} -12.3731 q^{43} +5.20342 q^{44} +0.274499 q^{45} -3.17975 q^{46} +10.7001 q^{47} +5.42772 q^{48} +1.00000 q^{49} -0.348082 q^{50} -2.13191 q^{51} +7.56353 q^{52} +12.4788 q^{53} +1.88170 q^{54} +2.76949 q^{55} -1.35015 q^{56} -6.99707 q^{57} +0.168765 q^{58} +3.92402 q^{59} +3.10179 q^{60} -13.6963 q^{61} -0.475182 q^{62} +0.274499 q^{63} -5.23716 q^{64} +4.02564 q^{65} +1.59149 q^{66} -10.4416 q^{67} +2.42624 q^{68} +15.0812 q^{69} -0.348082 q^{70} +13.1062 q^{71} -0.370615 q^{72} -7.82705 q^{73} +3.07966 q^{74} +1.65091 q^{75} +7.96311 q^{76} +2.76949 q^{77} +2.31334 q^{78} +9.94054 q^{79} -3.28771 q^{80} -8.10115 q^{81} +3.35685 q^{82} +1.57206 q^{83} +3.10179 q^{84} +1.29135 q^{85} +4.30686 q^{86} -0.800430 q^{87} -3.73924 q^{88} -5.68848 q^{89} -0.0955480 q^{90} +4.02564 q^{91} -17.1633 q^{92} +2.25373 q^{93} -3.72450 q^{94} +4.23831 q^{95} -6.34725 q^{96} +2.95243 q^{97} -0.348082 q^{98} +0.760221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−0.348082	−0.246131	−0.123066	−	0.992399i	$-0.539273\pi$
$2$	−0.348082	−0.246131	−0.123066	+	0.992399i	$0.539273\pi$
$3$	1.65091	0.953153	0.476576	−	0.879133i	$-0.341878\pi$
$3$	1.65091	0.953153	0.476576	+	0.879133i	$0.341878\pi$
$4$	−1.87884	−0.939419
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.574652	−0.234601
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.35015	0.477351
$9$	−0.274499	−0.0914995
$10$	0.348082	0.110073
$11$	−2.76949	−0.835032	−0.417516	−	0.908669i	$-0.637099\pi$
$11$	−2.76949	−0.835032	−0.417516	+	0.908669i	$0.637099\pi$
$12$	−3.10179	−0.895410
$13$	−4.02564	−1.11651	−0.558256	−	0.829669i	$-0.688529\pi$
$13$	−4.02564	−1.11651	−0.558256	+	0.829669i	$0.688529\pi$
$14$	0.348082	0.0930288
$15$	−1.65091	−0.426263
$16$	3.28771	0.821928
$17$	−1.29135	−0.313199	−0.156600	−	0.987662i	$-0.550053\pi$
$17$	−1.29135	−0.313199	−0.156600	+	0.987662i	$0.550053\pi$
$18$	0.0955480	0.0225209
$19$	−4.23831	−0.972336	−0.486168	−	0.873865i	$-0.661606\pi$
$19$	−4.23831	−0.972336	−0.486168	+	0.873865i	$0.661606\pi$
$20$	1.87884	0.420121
$21$	−1.65091	−0.360258
$22$	0.964009	0.205527
$23$	9.13506	1.90479	0.952396	−	0.304863i	$-0.0986107\pi$
$23$	9.13506	1.90479	0.952396	+	0.304863i	$0.0986107\pi$
$24$	2.22898	0.454989
$25$	1.00000	0.200000
$26$	1.40125	0.274808
$27$	−5.40590	−1.04037
$28$	1.87884	0.355067
$29$	−0.484842	−0.0900329	−0.0450164	−	0.998986i	$-0.514334\pi$
$29$	−0.484842	−0.0900329	−0.0450164	+	0.998986i	$0.514334\pi$
$30$	0.574652	0.104917
$31$	1.36515	0.245187	0.122594	−	0.992457i	$-0.460879\pi$
$31$	1.36515	0.245187	0.122594	+	0.992457i	$0.460879\pi$
$32$	−3.84470	−0.679654
$33$	−4.57218	−0.795914
$34$	0.449496	0.0770880
$35$	1.00000	0.169031
$36$	0.515739	0.0859564
$37$	−8.84752	−1.45452	−0.727262	−	0.686360i	$-0.759208\pi$
$37$	−8.84752	−1.45452	−0.727262	+	0.686360i	$0.759208\pi$
$38$	1.47528	0.239322
$39$	−6.64597	−1.06421
$40$	−1.35015	−0.213478
$41$	−9.64385	−1.50612	−0.753058	−	0.657954i	$-0.771422\pi$
$41$	−9.64385	−1.50612	−0.753058	+	0.657954i	$0.771422\pi$
$42$	0.574652	0.0886707
$43$	−12.3731	−1.88688	−0.943442	−	0.331538i	$-0.892432\pi$
$43$	−12.3731	−1.88688	−0.943442	+	0.331538i	$0.892432\pi$
$44$	5.20342	0.784446
$45$	0.274499	0.0409198
$46$	−3.17975	−0.468829
$47$	10.7001	1.56076	0.780382	−	0.625303i	$-0.215025\pi$
$47$	10.7001	1.56076	0.780382	+	0.625303i	$0.215025\pi$
$48$	5.42772	0.783424
$49$	1.00000	0.142857
$50$	−0.348082	−0.0492262
$51$	−2.13191	−0.298527
$52$	7.56353	1.04887
$53$	12.4788	1.71409	0.857047	−	0.515238i	$-0.172297\pi$
$53$	12.4788	1.71409	0.857047	+	0.515238i	$0.172297\pi$
$54$	1.88170	0.256066
$55$	2.76949	0.373438
$56$	−1.35015	−0.180422
$57$	−6.99707	−0.926785
$58$	0.168765	0.0221599
$59$	3.92402	0.510864	0.255432	−	0.966827i	$-0.417782\pi$
$59$	3.92402	0.510864	0.255432	+	0.966827i	$0.417782\pi$
$60$	3.10179	0.400440
$61$	−13.6963	−1.75364	−0.876819	−	0.480821i	$-0.840339\pi$
$61$	−13.6963	−1.75364	−0.876819	+	0.480821i	$0.840339\pi$
$62$	−0.475182	−0.0603482
$63$	0.274499	0.0345836
$64$	−5.23716	−0.654645
$65$	4.02564	0.499319
$66$	1.59149	0.195899
$67$	−10.4416	−1.27564	−0.637821	−	0.770185i	$-0.720164\pi$
$67$	−10.4416	−1.27564	−0.637821	+	0.770185i	$0.720164\pi$
$68$	2.42624	0.294225
$69$	15.0812	1.81556
$70$	−0.348082	−0.0416037
$71$	13.1062	1.55542	0.777709	−	0.628625i	$-0.216382\pi$
$71$	13.1062	1.55542	0.777709	+	0.628625i	$0.216382\pi$
$72$	−0.370615	−0.0436774
$73$	−7.82705	−0.916087	−0.458044	−	0.888930i	$-0.651450\pi$
$73$	−7.82705	−0.916087	−0.458044	+	0.888930i	$0.651450\pi$
$74$	3.07966	0.358004
$75$	1.65091	0.190631
$76$	7.96311	0.913431
$77$	2.76949	0.315613
$78$	2.31334	0.261934
$79$	9.94054	1.11840	0.559199	−	0.829034i	$-0.311109\pi$
$79$	9.94054	1.11840	0.559199	+	0.829034i	$0.311109\pi$
$80$	−3.28771	−0.367578
$81$	−8.10115	−0.900128
$82$	3.35685	0.370702
$83$	1.57206	0.172556	0.0862779	−	0.996271i	$-0.472503\pi$
$83$	1.57206	0.172556	0.0862779	+	0.996271i	$0.472503\pi$
$84$	3.10179	0.338433
$85$	1.29135	0.140067
$86$	4.30686	0.464421
$87$	−0.800430	−0.0858151
$88$	−3.73924	−0.398604
$89$	−5.68848	−0.602977	−0.301489	−	0.953470i	$-0.597484\pi$
$89$	−5.68848	−0.602977	−0.301489	+	0.953470i	$0.597484\pi$
$90$	−0.0955480	−0.0100716
$91$	4.02564	0.422002
$92$	−17.1633	−1.78940
$93$	2.25373	0.233701
$94$	−3.72450	−0.384153
$95$	4.23831	0.434842
$96$	−6.34725	−0.647814
$97$	2.95243	0.299774	0.149887	−	0.988703i	$-0.452109\pi$
$97$	2.95243	0.299774	0.149887	+	0.988703i	$0.452109\pi$
$98$	−0.348082	−0.0351616
$99$	0.760221	0.0764051
$100$	−1.87884	−0.187884
$101$	0.473144	0.0470796	0.0235398	−	0.999723i	$-0.492506\pi$
$101$	0.473144	0.0470796	0.0235398	+	0.999723i	$0.492506\pi$
$102$	0.742078	0.0734767
$103$	−1.18387	−0.116650	−0.0583249	−	0.998298i	$-0.518576\pi$
$103$	−1.18387	−0.116650	−0.0583249	+	0.998298i	$0.518576\pi$
$104$	−5.43523	−0.532969
$105$	1.65091	0.161112
$106$	−4.34364	−0.421892
$107$	−4.14838	−0.401039	−0.200520	−	0.979690i	$-0.564263\pi$
$107$	−4.14838	−0.401039	−0.200520	+	0.979690i	$0.564263\pi$
$108$	10.1568	0.977340
$109$	−8.68527	−0.831898	−0.415949	−	0.909388i	$-0.636551\pi$
$109$	−8.68527	−0.831898	−0.415949	+	0.909388i	$0.636551\pi$
$110$	−0.964009	−0.0919147
$111$	−14.6065	−1.38638
$112$	−3.28771	−0.310660
$113$	0.771176	0.0725461	0.0362731	−	0.999342i	$-0.488451\pi$
$113$	0.771176	0.0725461	0.0362731	+	0.999342i	$0.488451\pi$
$114$	2.43555	0.228110
$115$	−9.13506	−0.851849
$116$	0.910940	0.0845786
$117$	1.10503	0.102160
$118$	−1.36588	−0.125739
$119$	1.29135	0.118378
$120$	−2.22898	−0.203477
$121$	−3.32993	−0.302721
$122$	4.76745	0.431625
$123$	−15.9211	−1.43556
$124$	−2.56489	−0.230334
$125$	−1.00000	−0.0894427
$126$	−0.0955480	−0.00851209
$127$	2.21935	0.196936	0.0984678	−	0.995140i	$-0.468606\pi$
$127$	2.21935	0.196936	0.0984678	+	0.995140i	$0.468606\pi$
$128$	9.51236	0.840782
$129$	−20.4269	−1.79849
$130$	−1.40125	−0.122898
$131$	6.04214	0.527904	0.263952	−	0.964536i	$-0.414974\pi$
$131$	6.04214	0.527904	0.263952	+	0.964536i	$0.414974\pi$
$132$	8.59038	0.747697
$133$	4.23831	0.367508
$134$	3.63452	0.313975
$135$	5.40590	0.465266
$136$	−1.74352	−0.149506
$137$	1.56342	0.133572	0.0667858	−	0.997767i	$-0.478726\pi$
$137$	1.56342	0.133572	0.0667858	+	0.997767i	$0.478726\pi$
$138$	−5.24948	−0.446865
$139$	17.8864	1.51710	0.758552	−	0.651612i	$-0.225907\pi$
$139$	17.8864	1.51710	0.758552	+	0.651612i	$0.225907\pi$
$140$	−1.87884	−0.158791
$141$	17.6648	1.48765
$142$	−4.56203	−0.382837
$143$	11.1490	0.932324
$144$	−0.902473	−0.0752061
$145$	0.484842	0.0402639
$146$	2.72446	0.225478
$147$	1.65091	0.136165
$148$	16.6231	1.36641
$149$	20.1590	1.65149	0.825743	−	0.564046i	$-0.190756\pi$
$149$	20.1590	1.65149	0.825743	+	0.564046i	$0.190756\pi$
$150$	−0.574652	−0.0469201
$151$	−7.72037	−0.628275	−0.314137	−	0.949378i	$-0.601715\pi$
$151$	−7.72037	−0.628275	−0.314137	+	0.949378i	$0.601715\pi$
$152$	−5.72237	−0.464146
$153$	0.354474	0.0286576
$154$	−0.964009	−0.0776821
$155$	−1.36515	−0.109651
$156$	12.4867	0.999736
$157$	−0.968004	−0.0772551	−0.0386276	−	0.999254i	$-0.512299\pi$
$157$	−0.968004	−0.0772551	−0.0386276	+	0.999254i	$0.512299\pi$
$158$	−3.46012	−0.275272
$159$	20.6014	1.63379
$160$	3.84470	0.303950
$161$	−9.13506	−0.719944
$162$	2.81987	0.221550
$163$	15.3470	1.20207	0.601037	−	0.799221i	$-0.294755\pi$
$163$	15.3470	1.20207	0.601037	+	0.799221i	$0.294755\pi$
$164$	18.1192	1.41488
$165$	4.57218	0.355943
$166$	−0.547205	−0.0424714
$167$	22.2761	1.72377	0.861886	−	0.507101i	$-0.169283\pi$
$167$	22.2761	1.72377	0.861886	+	0.507101i	$0.169283\pi$
$168$	−2.22898	−0.171970
$169$	3.20579	0.246599
$170$	−0.449496	−0.0344748
$171$	1.16341	0.0889683
$172$	23.2471	1.77258
$173$	6.47862	0.492560	0.246280	−	0.969199i	$-0.420792\pi$
$173$	6.47862	0.492560	0.246280	+	0.969199i	$0.420792\pi$
$174$	0.278615	0.0211218
$175$	−1.00000	−0.0755929
$176$	−9.10529	−0.686337
$177$	6.47820	0.486931
$178$	1.98006	0.148411
$179$	5.31716	0.397423	0.198712	−	0.980058i	$-0.436324\pi$
$179$	5.31716	0.397423	0.198712	+	0.980058i	$0.436324\pi$
$180$	−0.515739	−0.0384409
$181$	14.6112	1.08604	0.543022	−	0.839719i	$-0.317280\pi$
$181$	14.6112	1.08604	0.543022	+	0.839719i	$0.317280\pi$
$182$	−1.40125	−0.103868
$183$	−22.6114	−1.67149
$184$	12.3337	0.909255
$185$	8.84752	0.650483
$186$	−0.784483	−0.0575211
$187$	3.57639	0.261531
$188$	−20.1037	−1.46621
$189$	5.40590	0.393221
$190$	−1.47528	−0.107028
$191$	−10.9499	−0.792307	−0.396153	−	0.918184i	$-0.629655\pi$
$191$	−10.9499	−0.792307	−0.396153	+	0.918184i	$0.629655\pi$
$192$	−8.64607	−0.623976
$193$	5.06928	0.364895	0.182447	−	0.983216i	$-0.441598\pi$
$193$	5.06928	0.364895	0.182447	+	0.983216i	$0.441598\pi$
$194$	−1.02769	−0.0737838
$195$	6.64597	0.475928
$196$	−1.87884	−0.134203
$197$	−24.0532	−1.71372	−0.856858	−	0.515552i	$-0.827587\pi$
$197$	−24.0532	−1.71372	−0.856858	+	0.515552i	$0.827587\pi$
$198$	−0.264619	−0.0188057
$199$	23.5440	1.66899	0.834495	−	0.551016i	$-0.185760\pi$
$199$	23.5440	1.66899	0.834495	+	0.551016i	$0.185760\pi$
$200$	1.35015	0.0954703
$201$	−17.2381	−1.21588
$202$	−0.164693	−0.0115877
$203$	0.484842	0.0340292
$204$	4.00551	0.280442
$205$	9.64385	0.673556
$206$	0.412083	0.0287112
$207$	−2.50756	−0.174288
$208$	−13.2352	−0.917693
$209$	11.7380	0.811932
$210$	−0.574652	−0.0396547
$211$	−9.38463	−0.646064	−0.323032	−	0.946388i	$-0.604702\pi$
$211$	−9.38463	−0.646064	−0.323032	+	0.946388i	$0.604702\pi$
$212$	−23.4456	−1.61025
$213$	21.6371	1.48255
$214$	1.44398	0.0987082
$215$	12.3731	0.843840
$216$	−7.29880	−0.496620
$217$	−1.36515	−0.0926721
$218$	3.02319	0.204756
$219$	−12.9218	−0.873171
$220$	−5.20342	−0.350815
$221$	5.19852	0.349690
$222$	5.08424	0.341232
$223$	29.4379	1.97131	0.985654	−	0.168780i	$-0.0539828\pi$
$223$	29.4379	1.97131	0.985654	+	0.168780i	$0.0539828\pi$
$224$	3.84470	0.256885
$225$	−0.274499	−0.0182999
$226$	−0.268432	−0.0178559
$227$	28.2046	1.87201	0.936004	−	0.351990i	$-0.114495\pi$
$227$	28.2046	1.87201	0.936004	+	0.351990i	$0.114495\pi$
$228$	13.1464	0.870639
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	3.17975	0.209667
$231$	4.57218	0.300827
$232$	−0.654611	−0.0429773
$233$	−19.5505	−1.28080	−0.640399	−	0.768042i	$-0.721231\pi$
$233$	−19.5505	−1.28080	−0.640399	+	0.768042i	$0.721231\pi$
$234$	−0.384642	−0.0251448
$235$	−10.7001	−0.697995
$236$	−7.37260	−0.479915
$237$	16.4109	1.06600
$238$	−0.449496	−0.0291365
$239$	−23.5780	−1.52513	−0.762567	−	0.646910i	$-0.776061\pi$
$239$	−23.5780	−1.52513	−0.762567	+	0.646910i	$0.776061\pi$
$240$	−5.42772	−0.350358
$241$	14.1632	0.912332	0.456166	−	0.889895i	$-0.349222\pi$
$241$	14.1632	0.912332	0.456166	+	0.889895i	$0.349222\pi$
$242$	1.15909	0.0745090
$243$	2.84343	0.182406
$244$	25.7332	1.64740
$245$	−1.00000	−0.0638877
$246$	5.54185	0.353336
$247$	17.0619	1.08562
$248$	1.84316	0.117041
$249$	2.59533	0.164472
$250$	0.348082	0.0220146
$251$	−3.95246	−0.249477	−0.124738	−	0.992190i	$-0.539809\pi$
$251$	−3.95246	−0.249477	−0.124738	+	0.992190i	$0.539809\pi$
$252$	−0.515739	−0.0324885
$253$	−25.2995	−1.59056
$254$	−0.772516	−0.0484720
$255$	2.13191	0.133505
$256$	7.16323	0.447702
$257$	−16.3399	−1.01925	−0.509627	−	0.860395i	$-0.670217\pi$
$257$	−16.3399	−1.01925	−0.509627	+	0.860395i	$0.670217\pi$
$258$	7.11024	0.442664
$259$	8.84752	0.549758
$260$	−7.56353	−0.469070
$261$	0.133088	0.00823797
$262$	−2.10316	−0.129934
$263$	22.4664	1.38534	0.692669	−	0.721256i	$-0.256435\pi$
$263$	22.4664	1.38534	0.692669	+	0.721256i	$0.256435\pi$
$264$	−6.17314	−0.379931
$265$	−12.4788	−0.766566
$266$	−1.47528	−0.0904552
$267$	−9.39116	−0.574730
$268$	19.6180	1.19836
$269$	30.7419	1.87437	0.937183	−	0.348838i	$-0.113424\pi$
$269$	30.7419	1.87437	0.937183	+	0.348838i	$0.113424\pi$
$270$	−1.88170	−0.114516
$271$	8.13752	0.494319	0.247160	−	0.968975i	$-0.420503\pi$
$271$	8.13752	0.494319	0.247160	+	0.968975i	$0.420503\pi$
$272$	−4.24560	−0.257427
$273$	6.64597	0.402232
$274$	−0.544196	−0.0328761
$275$	−2.76949	−0.167006
$276$	−28.3351	−1.70557
$277$	−4.84689	−0.291221	−0.145611	−	0.989342i	$-0.546515\pi$
$277$	−4.84689	−0.291221	−0.145611	+	0.989342i	$0.546515\pi$
$278$	−6.22593	−0.373407
$279$	−0.374730	−0.0224345
$280$	1.35015	0.0806871
$281$	25.3066	1.50967	0.754833	−	0.655916i	$-0.227718\pi$
$281$	25.3066	1.50967	0.754833	+	0.655916i	$0.227718\pi$
$282$	−6.14881	−0.366156
$283$	−15.6441	−0.929943	−0.464971	−	0.885326i	$-0.653935\pi$
$283$	−15.6441	−0.929943	−0.464971	+	0.885326i	$0.653935\pi$
$284$	−24.6244	−1.46119
$285$	6.99707	0.414471
$286$	−3.88076	−0.229474
$287$	9.64385	0.569259
$288$	1.05537	0.0621880
$289$	−15.3324	−0.901906
$290$	−0.168765	−0.00991020
$291$	4.87420	0.285731
$292$	14.7058	0.860590
$293$	22.6165	1.32127	0.660636	−	0.750707i	$-0.270287\pi$
$293$	22.6165	1.32127	0.660636	+	0.750707i	$0.270287\pi$
$294$	−0.574652	−0.0335144
$295$	−3.92402	−0.228465
$296$	−11.9455	−0.694319
$297$	14.9716	0.868739
$298$	−7.01697	−0.406482
$299$	−36.7745	−2.12672
$300$	−3.10179	−0.179082
$301$	12.3731	0.713175
$302$	2.68732	0.154638
$303$	0.781117	0.0448740
$304$	−13.9344	−0.799190
$305$	13.6963	0.784251
$306$	−0.123386	−0.00705352
$307$	−23.2243	−1.32548	−0.662741	−	0.748849i	$-0.730607\pi$
$307$	−23.2243	−1.32548	−0.662741	+	0.748849i	$0.730607\pi$
$308$	−5.20342	−0.296493
$309$	−1.95446	−0.111185
$310$	0.475182	0.0269885
$311$	10.9287	0.619709	0.309854	−	0.950784i	$-0.399720\pi$
$311$	10.9287	0.619709	0.309854	+	0.950784i	$0.399720\pi$
$312$	−8.97308	−0.508001
$313$	−20.9893	−1.18639	−0.593193	−	0.805060i	$-0.702133\pi$
$313$	−20.9893	−1.18639	−0.593193	+	0.805060i	$0.702133\pi$
$314$	0.336945	0.0190149
$315$	−0.274499	−0.0154662
$316$	−18.6767	−1.05064
$317$	−10.7214	−0.602176	−0.301088	−	0.953596i	$-0.597350\pi$
$317$	−10.7214	−0.602176	−0.301088	+	0.953596i	$0.597350\pi$
$318$	−7.17096	−0.402127
$319$	1.34276	0.0751804
$320$	5.23716	0.292766
$321$	−6.84860	−0.382252
$322$	3.17975	0.177201
$323$	5.47316	0.304535
$324$	15.2208	0.845598
$325$	−4.02564	−0.223302
$326$	−5.34203	−0.295868
$327$	−14.3386	−0.792926
$328$	−13.0207	−0.718947
$329$	−10.7001	−0.589913
$330$	−1.59149	−0.0876087
$331$	20.1848	1.10946	0.554728	−	0.832032i	$-0.312822\pi$
$331$	20.1848	1.10946	0.554728	+	0.832032i	$0.312822\pi$
$332$	−2.95364	−0.162102
$333$	2.42863	0.133088
$334$	−7.75389	−0.424274
$335$	10.4416	0.570484
$336$	−5.42772	−0.296106
$337$	21.0178	1.14491	0.572457	−	0.819935i	$-0.305990\pi$
$337$	21.0178	1.14491	0.572457	+	0.819935i	$0.305990\pi$
$338$	−1.11588	−0.0606957
$339$	1.27314	0.0691476
$340$	−2.42624	−0.131582
$341$	−3.78076	−0.204739
$342$	−0.404962	−0.0218979
$343$	−1.00000	−0.0539949
$344$	−16.7056	−0.900707
$345$	−15.0812	−0.811942
$346$	−2.25509	−0.121234
$347$	−23.0999	−1.24007	−0.620034	−	0.784575i	$-0.712881\pi$
$347$	−23.0999	−1.24007	−0.620034	+	0.784575i	$0.712881\pi$
$348$	1.50388	0.0806164
$349$	2.64085	0.141362	0.0706808	−	0.997499i	$-0.477483\pi$
$349$	2.64085	0.141362	0.0706808	+	0.997499i	$0.477483\pi$
$350$	0.348082	0.0186058
$351$	21.7622	1.16158
$352$	10.6479	0.567533
$353$	6.94384	0.369583	0.184792	−	0.982778i	$-0.440839\pi$
$353$	6.94384	0.369583	0.184792	+	0.982778i	$0.440839\pi$
$354$	−2.25494	−0.119849
$355$	−13.1062	−0.695604
$356$	10.6877	0.566449
$357$	2.13191	0.112832
$358$	−1.85081	−0.0978182
$359$	4.41837	0.233193	0.116596	−	0.993179i	$-0.462802\pi$
$359$	4.41837	0.233193	0.116596	+	0.993179i	$0.462802\pi$
$360$	0.370615	0.0195331
$361$	−1.03670	−0.0545633
$362$	−5.08590	−0.267309
$363$	−5.49741	−0.288539
$364$	−7.56353	−0.396437
$365$	7.82705	0.409687
$366$	7.87063	0.411404
$367$	−22.0409	−1.15053	−0.575264	−	0.817968i	$-0.695101\pi$
$367$	−22.0409	−1.15053	−0.575264	+	0.817968i	$0.695101\pi$
$368$	30.0335	1.56560
$369$	2.64722	0.137809
$370$	−3.07966	−0.160104
$371$	−12.4788	−0.647867
$372$	−4.23440	−0.219543
$373$	−17.1784	−0.889466	−0.444733	−	0.895663i	$-0.646701\pi$
$373$	−17.1784	−0.889466	−0.444733	+	0.895663i	$0.646701\pi$
$374$	−1.24488	−0.0643710
$375$	−1.65091	−0.0852526
$376$	14.4467	0.745033
$377$	1.95180	0.100523
$378$	−1.88170	−0.0967840
$379$	29.5824	1.51955	0.759774	−	0.650187i	$-0.225310\pi$
$379$	29.5824	1.51955	0.759774	+	0.650187i	$0.225310\pi$
$380$	−7.96311	−0.408499
$381$	3.66395	0.187710
$382$	3.81146	0.195011
$383$	12.9784	0.663163	0.331581	−	0.943427i	$-0.392418\pi$
$383$	12.9784	0.663163	0.331581	+	0.943427i	$0.392418\pi$
$384$	15.7040	0.801394
$385$	−2.76949	−0.141146
$386$	−1.76452	−0.0898119
$387$	3.39640	0.172649
$388$	−5.54715	−0.281614
$389$	−27.7396	−1.40645	−0.703226	−	0.710966i	$-0.748258\pi$
$389$	−27.7396	−1.40645	−0.703226	+	0.710966i	$0.748258\pi$
$390$	−2.31334	−0.117141
$391$	−11.7966	−0.596579
$392$	1.35015	0.0681931
$393$	9.97502	0.503173
$394$	8.37247	0.421799
$395$	−9.94054	−0.500163
$396$	−1.42833	−0.0717764
$397$	−2.49561	−0.125251	−0.0626256	−	0.998037i	$-0.519947\pi$
$397$	−2.49561	−0.125251	−0.0626256	+	0.998037i	$0.519947\pi$
$398$	−8.19524	−0.410790
$399$	6.99707	0.350292
$400$	3.28771	0.164386
$401$	−30.2728	−1.51175	−0.755876	−	0.654714i	$-0.772789\pi$
$401$	−30.2728	−1.51175	−0.755876	+	0.654714i	$0.772789\pi$
$402$	6.00027	0.299266
$403$	−5.49559	−0.273755
$404$	−0.888961	−0.0442275
$405$	8.10115	0.402550
$406$	−0.168765	−0.00837565
$407$	24.5031	1.21457
$408$	−2.87840	−0.142502
$409$	−21.9112	−1.08344	−0.541720	−	0.840559i	$-0.682227\pi$
$409$	−21.9112	−1.08344	−0.541720	+	0.840559i	$0.682227\pi$
$410$	−3.35685	−0.165783
$411$	2.58106	0.127314
$412$	2.22429	0.109583
$413$	−3.92402	−0.193088
$414$	0.872837	0.0428976
$415$	−1.57206	−0.0771693
$416$	15.4774	0.758841
$417$	29.5288	1.44603
$418$	−4.08577	−0.199842
$419$	30.5775	1.49381	0.746903	−	0.664933i	$-0.231540\pi$
$419$	30.5775	1.49381	0.746903	+	0.664933i	$0.231540\pi$
$420$	−3.10179	−0.151352
$421$	29.5723	1.44126	0.720632	−	0.693317i	$-0.243852\pi$
$421$	29.5723	1.44126	0.720632	+	0.693317i	$0.243852\pi$
$422$	3.26662	0.159017
$423$	−2.93715	−0.142809
$424$	16.8483	0.818225
$425$	−1.29135	−0.0626398
$426$	−7.53149	−0.364902
$427$	13.6963	0.662813
$428$	7.79414	0.376744
$429$	18.4059	0.888647
$430$	−4.30686	−0.207695
$431$	−17.8640	−0.860477	−0.430238	−	0.902715i	$-0.641571\pi$
$431$	−17.8640	−0.860477	−0.430238	+	0.902715i	$0.641571\pi$
$432$	−17.7731	−0.855106
$433$	−3.26672	−0.156989	−0.0784943	−	0.996915i	$-0.525011\pi$
$433$	−3.26672	−0.156989	−0.0784943	+	0.996915i	$0.525011\pi$
$434$	0.475182	0.0228095
$435$	0.800430	0.0383777
$436$	16.3182	0.781501
$437$	−38.7173	−1.85210
$438$	4.49783	0.214915
$439$	−15.6021	−0.744646	−0.372323	−	0.928103i	$-0.621439\pi$
$439$	−15.6021	−0.744646	−0.372323	+	0.928103i	$0.621439\pi$
$440$	3.73924	0.178261
$441$	−0.274499	−0.0130714
$442$	−1.80951	−0.0860697
$443$	−10.3872	−0.493511	−0.246756	−	0.969078i	$-0.579364\pi$
$443$	−10.3872	−0.493511	−0.246756	+	0.969078i	$0.579364\pi$
$444$	27.4432	1.30240
$445$	5.68848	0.269660
$446$	−10.2468	−0.485200
$447$	33.2806	1.57412
$448$	5.23716	0.247432
$449$	18.1077	0.854554	0.427277	−	0.904121i	$-0.359473\pi$
$449$	18.1077	0.854554	0.427277	+	0.904121i	$0.359473\pi$
$450$	0.0955480	0.00450418
$451$	26.7085	1.25766
$452$	−1.44892	−0.0681513
$453$	−12.7456	−0.598842
$454$	−9.81752	−0.460759
$455$	−4.02564	−0.188725
$456$	−9.44712	−0.442402
$457$	−7.66039	−0.358338	−0.179169	−	0.983818i	$-0.557341\pi$
$457$	−7.66039	−0.358338	−0.179169	+	0.983818i	$0.557341\pi$
$458$	−0.348082	−0.0162648
$459$	6.98092	0.325842
$460$	17.1633	0.800244
$461$	−2.52525	−0.117612	−0.0588062	−	0.998269i	$-0.518729\pi$
$461$	−2.52525	−0.117612	−0.0588062	+	0.998269i	$0.518729\pi$
$462$	−1.59149	−0.0740429
$463$	−4.10660	−0.190850	−0.0954249	−	0.995437i	$-0.530421\pi$
$463$	−4.10660	−0.190850	−0.0954249	+	0.995437i	$0.530421\pi$
$464$	−1.59402	−0.0740006
$465$	−2.25373	−0.104514
$466$	6.80519	0.315244
$467$	10.3398	0.478467	0.239234	−	0.970962i	$-0.423104\pi$
$467$	10.3398	0.478467	0.239234	+	0.970962i	$0.423104\pi$
$468$	−2.07618	−0.0959714
$469$	10.4416	0.482147
$470$	3.72450	0.171798
$471$	−1.59809	−0.0736359
$472$	5.29803	0.243862
$473$	34.2672	1.57561
$474$	−5.71235	−0.262377
$475$	−4.23831	−0.194467
$476$	−2.42624	−0.111207
$477$	−3.42541	−0.156839
$478$	8.20707	0.375383
$479$	20.6515	0.943591	0.471796	−	0.881708i	$-0.343606\pi$
$479$	20.6515	0.943591	0.471796	+	0.881708i	$0.343606\pi$
$480$	6.34725	0.289711
$481$	35.6170	1.62399
$482$	−4.92995	−0.224553
$483$	−15.0812	−0.686217
$484$	6.25640	0.284382
$485$	−2.95243	−0.134063
$486$	−0.989746	−0.0448958
$487$	4.55842	0.206562	0.103281	−	0.994652i	$-0.467066\pi$
$487$	4.55842	0.206562	0.103281	+	0.994652i	$0.467066\pi$
$488$	−18.4922	−0.837102
$489$	25.3366	1.14576
$490$	0.348082	0.0157247
$491$	5.08849	0.229641	0.114820	−	0.993386i	$-0.463371\pi$
$491$	5.08849	0.229641	0.114820	+	0.993386i	$0.463371\pi$
$492$	29.9132	1.34859
$493$	0.626102	0.0281982
$494$	−5.93895	−0.267206
$495$	−0.760221	−0.0341694
$496$	4.48821	0.201526
$497$	−13.1062	−0.587893
$498$	−0.903386	−0.0404817
$499$	44.2008	1.97870	0.989349	−	0.145564i	$-0.0464998\pi$
$499$	44.2008	1.97870	0.989349	+	0.145564i	$0.0464998\pi$
$500$	1.87884	0.0840242
$501$	36.7757	1.64302
$502$	1.37578	0.0614040
$503$	20.1739	0.899509	0.449754	−	0.893152i	$-0.351512\pi$
$503$	20.1739	0.899509	0.449754	+	0.893152i	$0.351512\pi$
$504$	0.370615	0.0165085
$505$	−0.473144	−0.0210546
$506$	8.80628	0.391487
$507$	5.29246	0.235047
$508$	−4.16981	−0.185005
$509$	−17.6989	−0.784489	−0.392245	−	0.919861i	$-0.628301\pi$
$509$	−17.6989	−0.784489	−0.392245	+	0.919861i	$0.628301\pi$
$510$	−0.742078	−0.0328598
$511$	7.82705	0.346249
$512$	−21.5181	−0.950975
$513$	22.9119	1.01158
$514$	5.68762	0.250870
$515$	1.18387	0.0521674
$516$	38.3789	1.68954
$517$	−29.6337	−1.30329
$518$	−3.07966	−0.135313
$519$	10.6956	0.469485
$520$	5.43523	0.238351
$521$	23.3969	1.02504	0.512518	−	0.858677i	$-0.328713\pi$
$521$	23.3969	1.02504	0.512518	+	0.858677i	$0.328713\pi$
$522$	−0.0463257	−0.00202762
$523$	−40.2731	−1.76102	−0.880510	−	0.474028i	$-0.842800\pi$
$523$	−40.2731	−1.76102	−0.880510	+	0.474028i	$0.842800\pi$
$524$	−11.3522	−0.495923
$525$	−1.65091	−0.0720516
$526$	−7.82014	−0.340975
$527$	−1.76288	−0.0767924
$528$	−15.0320	−0.654184
$529$	60.4494	2.62823
$530$	4.34364	0.188676
$531$	−1.07714	−0.0467438
$532$	−7.96311	−0.345244
$533$	38.8227	1.68160
$534$	3.26889	0.141459
$535$	4.14838	0.179350
$536$	−14.0977	−0.608929
$537$	8.77815	0.378805
$538$	−10.7007	−0.461340
$539$	−2.76949	−0.119290
$540$	−10.1568	−0.437080
$541$	−36.4197	−1.56580	−0.782902	−	0.622145i	$-0.786261\pi$
$541$	−36.4197	−1.56580	−0.782902	+	0.622145i	$0.786261\pi$
$542$	−2.83252	−0.121667
$543$	24.1218	1.03517
$544$	4.96486	0.212867
$545$	8.68527	0.372036
$546$	−2.31334	−0.0990019
$547$	−27.8495	−1.19076	−0.595380	−	0.803445i	$-0.702998\pi$
$547$	−27.8495	−1.19076	−0.595380	+	0.803445i	$0.702998\pi$
$548$	−2.93741	−0.125480
$549$	3.75963	0.160457
$550$	0.964009	0.0411055
$551$	2.05491	0.0875422
$552$	20.3619	0.866659
$553$	−9.94054	−0.422715
$554$	1.68712	0.0716786
$555$	14.6065	0.620010
$556$	−33.6057	−1.42520
$557$	−13.4272	−0.568928	−0.284464	−	0.958687i	$-0.591816\pi$
$557$	−13.4272	−0.568928	−0.284464	+	0.958687i	$0.591816\pi$
$558$	0.130437	0.00552183
$559$	49.8098	2.10673
$560$	3.28771	0.138931
$561$	5.90429	0.249279
$562$	−8.80878	−0.371576
$563$	−3.77083	−0.158922	−0.0794608	−	0.996838i	$-0.525320\pi$
$563$	−3.77083	−0.158922	−0.0794608	+	0.996838i	$0.525320\pi$
$564$	−33.1894	−1.39752
$565$	−0.771176	−0.0324436
$566$	5.44541	0.228888
$567$	8.10115	0.340217
$568$	17.6954	0.742481
$569$	−19.7635	−0.828531	−0.414265	−	0.910156i	$-0.635961\pi$
$569$	−19.7635	−0.828531	−0.414265	+	0.910156i	$0.635961\pi$
$570$	−2.43555	−0.102014
$571$	−2.38240	−0.0997003	−0.0498501	−	0.998757i	$-0.515874\pi$
$571$	−2.38240	−0.0997003	−0.0498501	+	0.998757i	$0.515874\pi$
$572$	−20.9471	−0.875843
$573$	−18.0773	−0.755189
$574$	−3.35685	−0.140112
$575$	9.13506	0.380958
$576$	1.43759	0.0598997
$577$	25.7501	1.07199	0.535996	−	0.844221i	$-0.319936\pi$
$577$	25.7501	1.07199	0.535996	+	0.844221i	$0.319936\pi$
$578$	5.33693	0.221987
$579$	8.36892	0.347801
$580$	−0.910940	−0.0378247
$581$	−1.57206	−0.0652200
$582$	−1.69662	−0.0703272
$583$	−34.5599	−1.43132
$584$	−10.5677	−0.437296
$585$	−1.10503	−0.0456875
$586$	−7.87240	−0.325206
$587$	11.5931	0.478499	0.239250	−	0.970958i	$-0.423099\pi$
$587$	11.5931	0.478499	0.239250	+	0.970958i	$0.423099\pi$
$588$	−3.10179	−0.127916
$589$	−5.78591	−0.238404
$590$	1.36588	0.0562324
$591$	−39.7096	−1.63343
$592$	−29.0881	−1.19551
$593$	11.2336	0.461310	0.230655	−	0.973036i	$-0.425913\pi$
$593$	11.2336	0.461310	0.230655	+	0.973036i	$0.425913\pi$
$594$	−5.21134	−0.213824
$595$	−1.29135	−0.0529403
$596$	−37.8754	−1.55144
$597$	38.8690	1.59080
$598$	12.8005	0.523453
$599$	−33.4577	−1.36705	−0.683523	−	0.729929i	$-0.739553\pi$
$599$	−33.4577	−1.36705	−0.683523	+	0.729929i	$0.739553\pi$
$600$	2.22898	0.0909978
$601$	5.22694	0.213211	0.106606	−	0.994301i	$-0.466002\pi$
$601$	5.22694	0.213211	0.106606	+	0.994301i	$0.466002\pi$
$602$	−4.30686	−0.175535
$603$	2.86620	0.116721
$604$	14.5053	0.590214
$605$	3.32993	0.135381
$606$	−0.271893	−0.0110449
$607$	25.8435	1.04896	0.524478	−	0.851424i	$-0.324261\pi$
$607$	25.8435	1.04896	0.524478	+	0.851424i	$0.324261\pi$
$608$	16.2950	0.660851
$609$	0.800430	0.0324351
$610$	−4.76745	−0.193028
$611$	−43.0746	−1.74261
$612$	−0.666000	−0.0269215
$613$	13.2598	0.535559	0.267779	−	0.963480i	$-0.413710\pi$
$613$	13.2598	0.535559	0.267779	+	0.963480i	$0.413710\pi$
$614$	8.08396	0.326242
$615$	15.9211	0.642002
$616$	3.73924	0.150658
$617$	13.4081	0.539789	0.269895	−	0.962890i	$-0.413011\pi$
$617$	13.4081	0.539789	0.269895	+	0.962890i	$0.413011\pi$
$618$	0.680311	0.0273661
$619$	−13.1842	−0.529919	−0.264959	−	0.964260i	$-0.585359\pi$
$619$	−13.1842	−0.529919	−0.264959	+	0.964260i	$0.585359\pi$
$620$	2.56489	0.103008
$621$	−49.3832	−1.98168
$622$	−3.80408	−0.152530
$623$	5.68848	0.227904
$624$	−21.8500	−0.874702
$625$	1.00000	0.0400000
$626$	7.30600	0.292006
$627$	19.3783	0.773895
$628$	1.81872	0.0725750
$629$	11.4253	0.455556
$630$	0.0955480	0.00380672
$631$	10.9698	0.436701	0.218351	−	0.975870i	$-0.429932\pi$
$631$	10.9698	0.436701	0.218351	+	0.975870i	$0.429932\pi$
$632$	13.4213	0.533869
$633$	−15.4932	−0.615798
$634$	3.73194	0.148214
$635$	−2.21935	−0.0880723
$636$	−38.7066	−1.53482
$637$	−4.02564	−0.159502
$638$	−0.467392	−0.0185042
$639$	−3.59763	−0.142320
$640$	−9.51236	−0.376009
$641$	27.0601	1.06881	0.534405	−	0.845229i	$-0.320536\pi$
$641$	27.0601	1.06881	0.534405	+	0.845229i	$0.320536\pi$
$642$	2.38388	0.0940840
$643$	−17.1305	−0.675562	−0.337781	−	0.941225i	$-0.609676\pi$
$643$	−17.1305	−0.675562	−0.337781	+	0.941225i	$0.609676\pi$
$644$	17.1633	0.676329
$645$	20.4269	0.804309
$646$	−1.90511	−0.0749554
$647$	−20.6424	−0.811537	−0.405769	−	0.913976i	$-0.632996\pi$
$647$	−20.6424	−0.811537	−0.405769	+	0.913976i	$0.632996\pi$
$648$	−10.9378	−0.429678
$649$	−10.8675	−0.426588
$650$	1.40125	0.0549617
$651$	−2.25373	−0.0883307
$652$	−28.8346	−1.12925
$653$	30.3111	1.18617	0.593083	−	0.805141i	$-0.297911\pi$
$653$	30.3111	1.18617	0.593083	+	0.805141i	$0.297911\pi$
$654$	4.99101	0.195164
$655$	−6.04214	−0.236086
$656$	−31.7062	−1.23792
$657$	2.14852	0.0838216
$658$	3.72450	0.145196
$659$	10.2551	0.399483	0.199741	−	0.979849i	$-0.435990\pi$
$659$	10.2551	0.399483	0.199741	+	0.979849i	$0.435990\pi$
$660$	−8.59038	−0.334380
$661$	−11.1029	−0.431852	−0.215926	−	0.976410i	$-0.569277\pi$
$661$	−11.1029	−0.431852	−0.215926	+	0.976410i	$0.569277\pi$
$662$	−7.02596	−0.273072
$663$	8.58229	0.333308
$664$	2.12252	0.0823698
$665$	−4.23831	−0.164355
$666$	−0.845363	−0.0327572
$667$	−4.42906	−0.171494
$668$	−41.8531	−1.61935
$669$	48.5993	1.87896
$670$	−3.63452	−0.140414
$671$	37.9319	1.46434
$672$	6.34725	0.244851
$673$	−22.5170	−0.867968	−0.433984	−	0.900921i	$-0.642893\pi$
$673$	−22.5170	−0.867968	−0.433984	+	0.900921i	$0.642893\pi$
$674$	−7.31593	−0.281799
$675$	−5.40590	−0.208073
$676$	−6.02316	−0.231660
$677$	−46.7821	−1.79798	−0.898990	−	0.437969i	$-0.855698\pi$
$677$	−46.7821	−1.79798	−0.898990	+	0.437969i	$0.855698\pi$
$678$	−0.443158	−0.0170194
$679$	−2.95243	−0.113304
$680$	1.74352	0.0668611
$681$	46.5633	1.78431
$682$	1.31601	0.0503927
$683$	32.6186	1.24812	0.624058	−	0.781378i	$-0.285483\pi$
$683$	32.6186	1.24812	0.624058	+	0.781378i	$0.285483\pi$
$684$	−2.18586	−0.0835785
$685$	−1.56342	−0.0597350
$686$	0.348082	0.0132898
$687$	1.65091	0.0629861
$688$	−40.6793	−1.55088
$689$	−50.2351	−1.91381
$690$	5.24948	0.199844
$691$	−35.6236	−1.35519	−0.677593	−	0.735437i	$-0.736977\pi$
$691$	−35.6236	−1.35519	−0.677593	+	0.735437i	$0.736977\pi$
$692$	−12.1723	−0.462721
$693$	−0.760221	−0.0288784
$694$	8.04066	0.305219
$695$	−17.8864	−0.678470
$696$	−1.08070	−0.0409640
$697$	12.4536	0.471714
$698$	−0.919233	−0.0347935
$699$	−32.2762	−1.22080
$700$	1.87884	0.0710134
$701$	−0.386601	−0.0146017	−0.00730086	−	0.999973i	$-0.502324\pi$
$701$	−0.386601	−0.0146017	−0.00730086	+	0.999973i	$0.502324\pi$
$702$	−7.57503	−0.285901
$703$	37.4986	1.41429
$704$	14.5043	0.546649
$705$	−17.6648	−0.665296
$706$	−2.41702	−0.0909659
$707$	−0.473144	−0.0177944
$708$	−12.1715	−0.457433
$709$	−15.4126	−0.578833	−0.289416	−	0.957203i	$-0.593461\pi$
$709$	−15.4126	−0.578833	−0.289416	+	0.957203i	$0.593461\pi$
$710$	4.56203	0.171210
$711$	−2.72866	−0.102333
$712$	−7.68032	−0.287832
$713$	12.4707	0.467031
$714$	−0.742078	−0.0277716
$715$	−11.1490	−0.416948
$716$	−9.99009	−0.373347
$717$	−38.9251	−1.45369
$718$	−1.53795	−0.0573959
$719$	27.9198	1.04123	0.520617	−	0.853790i	$-0.325702\pi$
$719$	27.9198	1.04123	0.520617	+	0.853790i	$0.325702\pi$
$720$	0.902473	0.0336332
$721$	1.18387	0.0440895
$722$	0.360858	0.0134297
$723$	23.3822	0.869592
$724$	−27.4521	−1.02025
$725$	−0.484842	−0.0180066
$726$	1.91355	0.0710185
$727$	−8.61249	−0.319420	−0.159710	−	0.987164i	$-0.551056\pi$
$727$	−8.61249	−0.319420	−0.159710	+	0.987164i	$0.551056\pi$
$728$	5.43523	0.201443
$729$	28.9977	1.07399
$730$	−2.72446	−0.100837
$731$	15.9781	0.590970
$732$	42.4832	1.57023
$733$	−8.06399	−0.297850	−0.148925	−	0.988848i	$-0.547581\pi$
$733$	−8.06399	−0.297850	−0.148925	+	0.988848i	$0.547581\pi$
$734$	7.67205	0.283181
$735$	−1.65091	−0.0608947
$736$	−35.1216	−1.29460
$737$	28.9178	1.06520
$738$	−0.921451	−0.0339191
$739$	3.33275	0.122597	0.0612986	−	0.998119i	$-0.480476\pi$
$739$	3.33275	0.122597	0.0612986	+	0.998119i	$0.480476\pi$
$740$	−16.6231	−0.611076
$741$	28.1677	1.03477
$742$	4.34364	0.159460
$743$	11.6989	0.429189	0.214595	−	0.976703i	$-0.431157\pi$
$743$	11.6989	0.429189	0.214595	+	0.976703i	$0.431157\pi$
$744$	3.04288	0.111558
$745$	−20.1590	−0.738567
$746$	5.97950	0.218925
$747$	−0.431528	−0.0157888
$748$	−6.71946	−0.245688
$749$	4.14838	0.151579
$750$	0.574652	0.0209833
$751$	2.68295	0.0979024	0.0489512	−	0.998801i	$-0.484412\pi$
$751$	2.68295	0.0979024	0.0489512	+	0.998801i	$0.484412\pi$
$752$	35.1787	1.28284
$753$	−6.52515	−0.237790
$754$	−0.679386	−0.0247418
$755$	7.72037	0.280973
$756$	−10.1568	−0.369400
$757$	44.6271	1.62200	0.811000	−	0.585046i	$-0.198924\pi$
$757$	44.6271	1.62200	0.811000	+	0.585046i	$0.198924\pi$
$758$	−10.2971	−0.374008
$759$	−41.7671	−1.51605
$760$	5.72237	0.207572
$761$	−5.35138	−0.193987	−0.0969937	−	0.995285i	$-0.530923\pi$
$761$	−5.35138	−0.193987	−0.0969937	+	0.995285i	$0.530923\pi$
$762$	−1.27535	−0.0462012
$763$	8.68527	0.314428
$764$	20.5731	0.744308
$765$	−0.354474	−0.0128161
$766$	−4.51753	−0.163225
$767$	−15.7967	−0.570386
$768$	11.8258	0.426728
$769$	6.87169	0.247800	0.123900	−	0.992295i	$-0.460460\pi$
$769$	6.87169	0.247800	0.123900	+	0.992295i	$0.460460\pi$
$770$	0.964009	0.0347405
$771$	−26.9757	−0.971505
$772$	−9.52436	−0.342789
$773$	−32.8170	−1.18035	−0.590174	−	0.807276i	$-0.700941\pi$
$773$	−32.8170	−1.18035	−0.590174	+	0.807276i	$0.700941\pi$
$774$	−1.18223	−0.0424943
$775$	1.36515	0.0490375
$776$	3.98624	0.143098
$777$	14.6065	0.524004
$778$	9.65564	0.346172
$779$	40.8737	1.46445
$780$	−12.4867	−0.447096
$781$	−36.2974	−1.29882
$782$	4.10618	0.146837
$783$	2.62101	0.0936671
$784$	3.28771	0.117418
$785$	0.968004	0.0345495
$786$	−3.47212	−0.123847
$787$	−24.5404	−0.874771	−0.437386	−	0.899274i	$-0.644096\pi$
$787$	−24.5404	−0.874771	−0.437386	+	0.899274i	$0.644096\pi$
$788$	45.1920	1.60990
$789$	37.0900	1.32044
$790$	3.46012	0.123106
$791$	−0.771176	−0.0274199
$792$	1.02642	0.0364721
$793$	55.1366	1.95796
$794$	0.868677	0.0308282
$795$	−20.6014	−0.730655
$796$	−44.2354	−1.56788
$797$	−6.43383	−0.227898	−0.113949	−	0.993487i	$-0.536350\pi$
$797$	−6.43383	−0.227898	−0.113949	+	0.993487i	$0.536350\pi$
$798$	−2.43555	−0.0862177
$799$	−13.8175	−0.488830
$800$	−3.84470	−0.135931
$801$	1.56148	0.0551721
$802$	10.5374	0.372089
$803$	21.6769	0.764963
$804$	32.3876	1.14222
$805$	9.13506	0.321969
$806$	1.91291	0.0673795
$807$	50.7521	1.78656
$808$	0.638817	0.0224735
$809$	5.05570	0.177749	0.0888744	−	0.996043i	$-0.471673\pi$
$809$	5.05570	0.177749	0.0888744	+	0.996043i	$0.471673\pi$
$810$	−2.81987	−0.0990800
$811$	−16.4271	−0.576833	−0.288416	−	0.957505i	$-0.593129\pi$
$811$	−16.4271	−0.576833	−0.288416	+	0.957505i	$0.593129\pi$
$812$	−0.910940	−0.0319677
$813$	13.4343	0.471162
$814$	−8.52910	−0.298945
$815$	−15.3470	−0.537584
$816$	−7.00910	−0.245367
$817$	52.4412	1.83468
$818$	7.62689	0.266668
$819$	−1.10503	−0.0386130
$820$	−18.1192	−0.632751
$821$	9.33738	0.325877	0.162938	−	0.986636i	$-0.447903\pi$
$821$	9.33738	0.325877	0.162938	+	0.986636i	$0.447903\pi$
$822$	−0.898419	−0.0313360
$823$	10.5883	0.369083	0.184542	−	0.982825i	$-0.440920\pi$
$823$	10.5883	0.369083	0.184542	+	0.982825i	$0.440920\pi$
$824$	−1.59840	−0.0556830
$825$	−4.57218	−0.159183
$826$	1.36588	0.0475251
$827$	12.2458	0.425829	0.212914	−	0.977071i	$-0.431704\pi$
$827$	12.2458	0.425829	0.212914	+	0.977071i	$0.431704\pi$
$828$	4.71130	0.163729
$829$	−14.2996	−0.496645	−0.248322	−	0.968677i	$-0.579879\pi$
$829$	−14.2996	−0.496645	−0.248322	+	0.968677i	$0.579879\pi$
$830$	0.547205	0.0189938
$831$	−8.00178	−0.277579
$832$	21.0829	0.730919
$833$	−1.29135	−0.0447427
$834$	−10.2785	−0.355914
$835$	−22.2761	−0.770895
$836$	−22.0537	−0.762745
$837$	−7.37984	−0.255085
$838$	−10.6435	−0.367672
$839$	44.0677	1.52139	0.760693	−	0.649112i	$-0.224859\pi$
$839$	44.0677	1.52139	0.760693	+	0.649112i	$0.224859\pi$
$840$	2.22898	0.0769072
$841$	−28.7649	−0.991894
$842$	−10.2936	−0.354740
$843$	41.7789	1.43894
$844$	17.6322	0.606926
$845$	−3.20579	−0.110282
$846$	1.02237	0.0351498
$847$	3.32993	0.114418
$848$	41.0267	1.40886
$849$	−25.8269	−0.886378
$850$	0.449496	0.0154176
$851$	−80.8227	−2.77057
$852$	−40.6527	−1.39274
$853$	41.8305	1.43225	0.716125	−	0.697972i	$-0.245914\pi$
$853$	41.8305	1.43225	0.716125	+	0.697972i	$0.245914\pi$
$854$	−4.76745	−0.163139
$855$	−1.16341	−0.0397878
$856$	−5.60095	−0.191437
$857$	−42.3877	−1.44793	−0.723967	−	0.689834i	$-0.757683\pi$
$857$	−42.3877	−1.44793	−0.723967	+	0.689834i	$0.757683\pi$
$858$	−6.40677	−0.218724
$859$	44.3753	1.51407	0.757034	−	0.653376i	$-0.226648\pi$
$859$	44.3753	1.51407	0.757034	+	0.653376i	$0.226648\pi$
$860$	−23.2471	−0.792720
$861$	15.9211	0.542590
$862$	6.21812	0.211790
$863$	11.8987	0.405038	0.202519	−	0.979278i	$-0.435087\pi$
$863$	11.8987	0.405038	0.202519	+	0.979278i	$0.435087\pi$
$864$	20.7841	0.707088
$865$	−6.47862	−0.220280
$866$	1.13709	0.0386398
$867$	−25.3124	−0.859655
$868$	2.56489	0.0870580
$869$	−27.5302	−0.933898
$870$	−0.278615	−0.00944594
$871$	42.0340	1.42427
$872$	−11.7265	−0.397108
$873$	−0.810439	−0.0274292
$874$	13.4768	0.455859
$875$	1.00000	0.0338062
$876$	24.2779	0.820274
$877$	11.9095	0.402154	0.201077	−	0.979575i	$-0.435556\pi$
$877$	11.9095	0.402154	0.201077	+	0.979575i	$0.435556\pi$
$878$	5.43079	0.183280
$879$	37.3378	1.25937
$880$	9.10529	0.306939
$881$	−4.97365	−0.167567	−0.0837833	−	0.996484i	$-0.526700\pi$
$881$	−4.97365	−0.167567	−0.0837833	+	0.996484i	$0.526700\pi$
$882$	0.0955480	0.00321727
$883$	−13.4365	−0.452176	−0.226088	−	0.974107i	$-0.572594\pi$
$883$	−13.4365	−0.452176	−0.226088	+	0.974107i	$0.572594\pi$
$884$	−9.76719	−0.328506
$885$	−6.47820	−0.217762
$886$	3.61560	0.121468
$887$	52.7196	1.77015	0.885075	−	0.465449i	$-0.154107\pi$
$887$	52.7196	1.77015	0.885075	+	0.465449i	$0.154107\pi$
$888$	−19.7210	−0.661792
$889$	−2.21935	−0.0744347
$890$	−1.98006	−0.0663716
$891$	22.4361	0.751636
$892$	−55.3091	−1.85188
$893$	−45.3502	−1.51759
$894$	−11.5844	−0.387440
$895$	−5.31716	−0.177733
$896$	−9.51236	−0.317786
$897$	−60.7113	−2.02709
$898$	−6.30295	−0.210332
$899$	−0.661880	−0.0220749
$900$	0.515739	0.0171913
$901$	−16.1145	−0.536853
$902$	−9.29676	−0.309548
$903$	20.4269	0.679765
$904$	1.04121	0.0346300
$905$	−14.6112	−0.485693
$906$	4.43652	0.147394
$907$	−46.6533	−1.54910	−0.774548	−	0.632515i	$-0.782023\pi$
$907$	−46.6533	−1.54910	−0.774548	+	0.632515i	$0.782023\pi$
$908$	−52.9920	−1.75860
$909$	−0.129877	−0.00430776
$910$	1.40125	0.0464511
$911$	−50.0716	−1.65895	−0.829473	−	0.558546i	$-0.811359\pi$
$911$	−50.0716	−1.65895	−0.829473	+	0.558546i	$0.811359\pi$
$912$	−23.0044	−0.761751
$913$	−4.35380	−0.144090
$914$	2.66644	0.0881981
$915$	22.6114	0.747511
$916$	−1.87884	−0.0620786
$917$	−6.04214	−0.199529
$918$	−2.42993	−0.0801997
$919$	6.62344	0.218487	0.109244	−	0.994015i	$-0.465157\pi$
$919$	6.62344	0.218487	0.109244	+	0.994015i	$0.465157\pi$
$920$	−12.3337	−0.406631
$921$	−38.3412	−1.26339
$922$	0.878992	0.0289481
$923$	−52.7608	−1.73664
$924$	−8.59038	−0.282603
$925$	−8.84752	−0.290905
$926$	1.42943	0.0469741
$927$	0.324970	0.0106734
$928$	1.86407	0.0611912
$929$	−19.3548	−0.635010	−0.317505	−	0.948257i	$-0.602845\pi$
$929$	−19.3548	−0.635010	−0.317505	+	0.948257i	$0.602845\pi$
$930$	0.784483	0.0257242
$931$	−4.23831	−0.138905
$932$	36.7323	1.20321
$933$	18.0423	0.590677
$934$	−3.59909	−0.117766
$935$	−3.57639	−0.116960
$936$	1.49196	0.0487664
$937$	−0.983655	−0.0321346	−0.0160673	−	0.999871i	$-0.505115\pi$
$937$	−0.983655	−0.0321346	−0.0160673	+	0.999871i	$0.505115\pi$
$938$	−3.63452	−0.118671
$939$	−34.6514	−1.13081
$940$	20.1037	0.655710
$941$	33.0903	1.07871	0.539357	−	0.842077i	$-0.318667\pi$
$941$	33.0903	1.07871	0.539357	+	0.842077i	$0.318667\pi$
$942$	0.556265	0.0181241
$943$	−88.0972	−2.86884
$944$	12.9011	0.419894
$945$	−5.40590	−0.175854
$946$	−11.9278	−0.387806
$947$	54.3380	1.76575	0.882874	−	0.469610i	$-0.155606\pi$
$947$	54.3380	1.76575	0.882874	+	0.469610i	$0.155606\pi$
$948$	−30.8335	−1.00142
$949$	31.5089	1.02282
$950$	1.47528	0.0478644
$951$	−17.7001	−0.573965
$952$	1.74352	0.0565080
$953$	−9.83560	−0.318606	−0.159303	−	0.987230i	$-0.550925\pi$
$953$	−9.83560	−0.318606	−0.159303	+	0.987230i	$0.550925\pi$
$954$	1.19232	0.0386029
$955$	10.9499	0.354330
$956$	44.2992	1.43274
$957$	2.21678	0.0716584
$958$	−7.18841	−0.232247
$959$	−1.56342	−0.0504853
$960$	8.64607	0.279051
$961$	−29.1364	−0.939883
$962$	−12.3976	−0.399715
$963$	1.13873	0.0366949
$964$	−26.6104	−0.857062
$965$	−5.06928	−0.163186
$966$	5.24948	0.168899
$967$	5.11383	0.164450	0.0822248	−	0.996614i	$-0.473797\pi$
$967$	5.11383	0.164450	0.0822248	+	0.996614i	$0.473797\pi$
$968$	−4.49592	−0.144504
$969$	9.03568	0.290268
$970$	1.02769	0.0329971
$971$	−38.3252	−1.22991	−0.614957	−	0.788561i	$-0.710827\pi$
$971$	−38.3252	−1.22991	−0.614957	+	0.788561i	$0.710827\pi$
$972$	−5.34234	−0.171356
$973$	−17.8864	−0.573412
$974$	−1.58670	−0.0508412
$975$	−6.64597	−0.212841
$976$	−45.0297	−1.44136
$977$	6.08843	0.194786	0.0973930	−	0.995246i	$-0.468950\pi$
$977$	6.08843	0.194786	0.0973930	+	0.995246i	$0.468950\pi$
$978$	−8.81921	−0.282007
$979$	15.7542	0.503506
$980$	1.87884	0.0600173
$981$	2.38410	0.0761183
$982$	−1.77121	−0.0565217
$983$	50.7106	1.61742	0.808708	−	0.588210i	$-0.200167\pi$
$983$	50.7106	1.61742	0.808708	+	0.588210i	$0.200167\pi$
$984$	−21.4960	−0.685266
$985$	24.0532	0.766397
$986$	−0.217935	−0.00694046
$987$	−17.6648	−0.562278
$988$	−32.0566	−1.01986
$989$	−113.029	−3.59412
$990$	0.264619	0.00841015
$991$	14.7178	0.467525	0.233763	−	0.972294i	$-0.424896\pi$
$991$	14.7178	0.467525	0.233763	+	0.972294i	$0.424896\pi$
$992$	−5.24858	−0.166642
$993$	33.3232	1.05748
$994$	4.56203	0.144699
$995$	−23.5440	−0.746395
$996$	−4.87620	−0.154508
$997$	−9.38007	−0.297070	−0.148535	−	0.988907i	$-0.547456\pi$
$997$	−9.38007	−0.297070	−0.148535	+	0.988907i	$0.547456\pi$
$998$	−15.3855	−0.487019
$999$	47.8288	1.51324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.29	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.29	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +O(q^{10})\)	\(q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +0.348082 q^{10} -2.76949 q^{11} -3.10179 q^{12} -4.02564 q^{13} +0.348082 q^{14} -1.65091 q^{15} +3.28771 q^{16} -1.29135 q^{17} +0.0955480 q^{18} -4.23831 q^{19} +1.87884 q^{20} -1.65091 q^{21} +0.964009 q^{22} +9.13506 q^{23} +2.22898 q^{24} +1.00000 q^{25} +1.40125 q^{26} -5.40590 q^{27} +1.87884 q^{28} -0.484842 q^{29} +0.574652 q^{30} +1.36515 q^{31} -3.84470 q^{32} -4.57218 q^{33} +0.449496 q^{34} +1.00000 q^{35} +0.515739 q^{36} -8.84752 q^{37} +1.47528 q^{38} -6.64597 q^{39} -1.35015 q^{40} -9.64385 q^{41} +0.574652 q^{42} -12.3731 q^{43} +5.20342 q^{44} +0.274499 q^{45} -3.17975 q^{46} +10.7001 q^{47} +5.42772 q^{48} +1.00000 q^{49} -0.348082 q^{50} -2.13191 q^{51} +7.56353 q^{52} +12.4788 q^{53} +1.88170 q^{54} +2.76949 q^{55} -1.35015 q^{56} -6.99707 q^{57} +0.168765 q^{58} +3.92402 q^{59} +3.10179 q^{60} -13.6963 q^{61} -0.475182 q^{62} +0.274499 q^{63} -5.23716 q^{64} +4.02564 q^{65} +1.59149 q^{66} -10.4416 q^{67} +2.42624 q^{68} +15.0812 q^{69} -0.348082 q^{70} +13.1062 q^{71} -0.370615 q^{72} -7.82705 q^{73} +3.07966 q^{74} +1.65091 q^{75} +7.96311 q^{76} +2.76949 q^{77} +2.31334 q^{78} +9.94054 q^{79} -3.28771 q^{80} -8.10115 q^{81} +3.35685 q^{82} +1.57206 q^{83} +3.10179 q^{84} +1.29135 q^{85} +4.30686 q^{86} -0.800430 q^{87} -3.73924 q^{88} -5.68848 q^{89} -0.0955480 q^{90} +4.02564 q^{91} -17.1633 q^{92} +2.25373 q^{93} -3.72450 q^{94} +4.23831 q^{95} -6.34725 q^{96} +2.95243 q^{97} -0.348082 q^{98} +0.760221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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