LMFDB - Embedded newform 8018.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.89970 q^{3} +1.00000 q^{4} +0.525736 q^{5} -1.89970 q^{6} -0.379709 q^{7} +1.00000 q^{8} +0.608871 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.89970 q^{3} +1.00000 q^{4} +0.525736 q^{5} -1.89970 q^{6} -0.379709 q^{7} +1.00000 q^{8} +0.608871 q^{9} +0.525736 q^{10} -2.26183 q^{11} -1.89970 q^{12} -0.587660 q^{13} -0.379709 q^{14} -0.998743 q^{15} +1.00000 q^{16} +1.06043 q^{17} +0.608871 q^{18} -1.00000 q^{19} +0.525736 q^{20} +0.721334 q^{21} -2.26183 q^{22} -1.75691 q^{23} -1.89970 q^{24} -4.72360 q^{25} -0.587660 q^{26} +4.54243 q^{27} -0.379709 q^{28} +8.53707 q^{29} -0.998743 q^{30} +1.41499 q^{31} +1.00000 q^{32} +4.29680 q^{33} +1.06043 q^{34} -0.199627 q^{35} +0.608871 q^{36} +7.02354 q^{37} -1.00000 q^{38} +1.11638 q^{39} +0.525736 q^{40} +1.12034 q^{41} +0.721334 q^{42} +0.392283 q^{43} -2.26183 q^{44} +0.320106 q^{45} -1.75691 q^{46} +4.10208 q^{47} -1.89970 q^{48} -6.85582 q^{49} -4.72360 q^{50} -2.01450 q^{51} -0.587660 q^{52} -2.04355 q^{53} +4.54243 q^{54} -1.18913 q^{55} -0.379709 q^{56} +1.89970 q^{57} +8.53707 q^{58} +9.24999 q^{59} -0.998743 q^{60} -9.71496 q^{61} +1.41499 q^{62} -0.231193 q^{63} +1.00000 q^{64} -0.308954 q^{65} +4.29680 q^{66} +0.627289 q^{67} +1.06043 q^{68} +3.33761 q^{69} -0.199627 q^{70} -12.8438 q^{71} +0.608871 q^{72} -9.16748 q^{73} +7.02354 q^{74} +8.97344 q^{75} -1.00000 q^{76} +0.858836 q^{77} +1.11638 q^{78} +13.5143 q^{79} +0.525736 q^{80} -10.4559 q^{81} +1.12034 q^{82} -9.65001 q^{83} +0.721334 q^{84} +0.557505 q^{85} +0.392283 q^{86} -16.2179 q^{87} -2.26183 q^{88} -17.4338 q^{89} +0.320106 q^{90} +0.223139 q^{91} -1.75691 q^{92} -2.68806 q^{93} +4.10208 q^{94} -0.525736 q^{95} -1.89970 q^{96} +6.85937 q^{97} -6.85582 q^{98} -1.37716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.89970	−1.09679	−0.548397	−	0.836218i	$-0.684762\pi$
$3$	−1.89970	−1.09679	−0.548397	+	0.836218i	$0.684762\pi$
$4$	1.00000	0.500000
$5$	0.525736	0.235116	0.117558	−	0.993066i	$-0.462493\pi$
$5$	0.525736	0.235116	0.117558	+	0.993066i	$0.462493\pi$
$6$	−1.89970	−0.775550
$7$	−0.379709	−0.143516	−0.0717582	−	0.997422i	$-0.522861\pi$
$7$	−0.379709	−0.143516	−0.0717582	+	0.997422i	$0.522861\pi$
$8$	1.00000	0.353553
$9$	0.608871	0.202957
$10$	0.525736	0.166252
$11$	−2.26183	−0.681967	−0.340983	−	0.940069i	$-0.610760\pi$
$11$	−2.26183	−0.681967	−0.340983	+	0.940069i	$0.610760\pi$
$12$	−1.89970	−0.548397
$13$	−0.587660	−0.162987	−0.0814937	−	0.996674i	$-0.525969\pi$
$13$	−0.587660	−0.162987	−0.0814937	+	0.996674i	$0.525969\pi$
$14$	−0.379709	−0.101481
$15$	−0.998743	−0.257874
$16$	1.00000	0.250000
$17$	1.06043	0.257192	0.128596	−	0.991697i	$-0.458953\pi$
$17$	1.06043	0.257192	0.128596	+	0.991697i	$0.458953\pi$
$18$	0.608871	0.143512
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.525736	0.117558
$21$	0.721334	0.157408
$22$	−2.26183	−0.482223
$23$	−1.75691	−0.366341	−0.183171	−	0.983081i	$-0.558636\pi$
$23$	−1.75691	−0.366341	−0.183171	+	0.983081i	$0.558636\pi$
$24$	−1.89970	−0.387775
$25$	−4.72360	−0.944720
$26$	−0.587660	−0.115250
$27$	4.54243	0.874192
$28$	−0.379709	−0.0717582
$29$	8.53707	1.58529	0.792647	−	0.609681i	$-0.208702\pi$
$29$	8.53707	1.58529	0.792647	+	0.609681i	$0.208702\pi$
$30$	−0.998743	−0.182345
$31$	1.41499	0.254139	0.127070	−	0.991894i	$-0.459443\pi$
$31$	1.41499	0.254139	0.127070	+	0.991894i	$0.459443\pi$
$32$	1.00000	0.176777
$33$	4.29680	0.747977
$34$	1.06043	0.181862
$35$	−0.199627	−0.0337431
$36$	0.608871	0.101478
$37$	7.02354	1.15466	0.577332	−	0.816510i	$-0.304094\pi$
$37$	7.02354	1.15466	0.577332	+	0.816510i	$0.304094\pi$
$38$	−1.00000	−0.162221
$39$	1.11638	0.178764
$40$	0.525736	0.0831262
$41$	1.12034	0.174967	0.0874837	−	0.996166i	$-0.472117\pi$
$41$	1.12034	0.174967	0.0874837	+	0.996166i	$0.472117\pi$
$42$	0.721334	0.111304
$43$	0.392283	0.0598226	0.0299113	−	0.999553i	$-0.490478\pi$
$43$	0.392283	0.0598226	0.0299113	+	0.999553i	$0.490478\pi$
$44$	−2.26183	−0.340983
$45$	0.320106	0.0477185
$46$	−1.75691	−0.259042
$47$	4.10208	0.598349	0.299175	−	0.954198i	$-0.403289\pi$
$47$	4.10208	0.598349	0.299175	+	0.954198i	$0.403289\pi$
$48$	−1.89970	−0.274198
$49$	−6.85582	−0.979403
$50$	−4.72360	−0.668018
$51$	−2.01450	−0.282086
$52$	−0.587660	−0.0814937
$53$	−2.04355	−0.280704	−0.140352	−	0.990102i	$-0.544823\pi$
$53$	−2.04355	−0.280704	−0.140352	+	0.990102i	$0.544823\pi$
$54$	4.54243	0.618147
$55$	−1.18913	−0.160342
$56$	−0.379709	−0.0507407
$57$	1.89970	0.251622
$58$	8.53707	1.12097
$59$	9.24999	1.20425	0.602123	−	0.798403i	$-0.294322\pi$
$59$	9.24999	1.20425	0.602123	+	0.798403i	$0.294322\pi$
$60$	−0.998743	−0.128937
$61$	−9.71496	−1.24387	−0.621937	−	0.783068i	$-0.713654\pi$
$61$	−9.71496	−1.24387	−0.621937	+	0.783068i	$0.713654\pi$
$62$	1.41499	0.179704
$63$	−0.231193	−0.0291276
$64$	1.00000	0.125000
$65$	−0.308954	−0.0383210
$66$	4.29680	0.528900
$67$	0.627289	0.0766356	0.0383178	−	0.999266i	$-0.487800\pi$
$67$	0.627289	0.0766356	0.0383178	+	0.999266i	$0.487800\pi$
$68$	1.06043	0.128596
$69$	3.33761	0.401801
$70$	−0.199627	−0.0238599
$71$	−12.8438	−1.52428	−0.762142	−	0.647410i	$-0.775852\pi$
$71$	−12.8438	−1.52428	−0.762142	+	0.647410i	$0.775852\pi$
$72$	0.608871	0.0717561
$73$	−9.16748	−1.07297	−0.536486	−	0.843909i	$-0.680249\pi$
$73$	−9.16748	−1.07297	−0.536486	+	0.843909i	$0.680249\pi$
$74$	7.02354	0.816470
$75$	8.97344	1.03616
$76$	−1.00000	−0.114708
$77$	0.858836	0.0978734
$78$	1.11638	0.126405
$79$	13.5143	1.52048	0.760239	−	0.649643i	$-0.225082\pi$
$79$	13.5143	1.52048	0.760239	+	0.649643i	$0.225082\pi$
$80$	0.525736	0.0587791
$81$	−10.4559	−1.16177
$82$	1.12034	0.123721
$83$	−9.65001	−1.05923	−0.529613	−	0.848239i	$-0.677663\pi$
$83$	−9.65001	−1.05923	−0.529613	+	0.848239i	$0.677663\pi$
$84$	0.721334	0.0787039
$85$	0.557505	0.0604700
$86$	0.392283	0.0423010
$87$	−16.2179	−1.73874
$88$	−2.26183	−0.241112
$89$	−17.4338	−1.84798	−0.923990	−	0.382415i	$-0.875092\pi$
$89$	−17.4338	−1.84798	−0.923990	+	0.382415i	$0.875092\pi$
$90$	0.320106	0.0337421
$91$	0.223139	0.0233914
$92$	−1.75691	−0.183171
$93$	−2.68806	−0.278738
$94$	4.10208	0.423097
$95$	−0.525736	−0.0539394
$96$	−1.89970	−0.193888
$97$	6.85937	0.696464	0.348232	−	0.937408i	$-0.386782\pi$
$97$	6.85937	0.696464	0.348232	+	0.937408i	$0.386782\pi$
$98$	−6.85582	−0.692543
$99$	−1.37716	−0.138410
$100$	−4.72360	−0.472360
$101$	−4.67666	−0.465345	−0.232672	−	0.972555i	$-0.574747\pi$
$101$	−4.67666	−0.465345	−0.232672	+	0.972555i	$0.574747\pi$
$102$	−2.01450	−0.199465
$103$	−8.00413	−0.788670	−0.394335	−	0.918967i	$-0.629025\pi$
$103$	−8.00413	−0.788670	−0.394335	+	0.918967i	$0.629025\pi$
$104$	−0.587660	−0.0576248
$105$	0.379231	0.0370092
$106$	−2.04355	−0.198487
$107$	8.49736	0.821470	0.410735	−	0.911755i	$-0.365272\pi$
$107$	8.49736	0.821470	0.410735	+	0.911755i	$0.365272\pi$
$108$	4.54243	0.437096
$109$	−0.597719	−0.0572511	−0.0286255	−	0.999590i	$-0.509113\pi$
$109$	−0.597719	−0.0572511	−0.0286255	+	0.999590i	$0.509113\pi$
$110$	−1.18913	−0.113379
$111$	−13.3426	−1.26643
$112$	−0.379709	−0.0358791
$113$	−6.43871	−0.605703	−0.302851	−	0.953038i	$-0.597939\pi$
$113$	−6.43871	−0.605703	−0.302851	+	0.953038i	$0.597939\pi$
$114$	1.89970	0.177923
$115$	−0.923672	−0.0861329
$116$	8.53707	0.792647
$117$	−0.357809	−0.0330794
$118$	9.24999	0.851531
$119$	−0.402654	−0.0369112
$120$	−0.998743	−0.0911723
$121$	−5.88413	−0.534921
$122$	−9.71496	−0.879551
$123$	−2.12831	−0.191903
$124$	1.41499	0.127070
$125$	−5.11205	−0.457236
$126$	−0.231193	−0.0205964
$127$	13.2737	1.17785	0.588924	−	0.808188i	$-0.299552\pi$
$127$	13.2737	1.17785	0.588924	+	0.808188i	$0.299552\pi$
$128$	1.00000	0.0883883
$129$	−0.745221	−0.0656131
$130$	−0.308954	−0.0270971
$131$	15.2992	1.33669	0.668347	−	0.743850i	$-0.267002\pi$
$131$	15.2992	1.33669	0.668347	+	0.743850i	$0.267002\pi$
$132$	4.29680	0.373989
$133$	0.379709	0.0329249
$134$	0.627289	0.0541896
$135$	2.38812	0.205537
$136$	1.06043	0.0909309
$137$	−17.7853	−1.51950	−0.759751	−	0.650214i	$-0.774679\pi$
$137$	−17.7853	−1.51950	−0.759751	+	0.650214i	$0.774679\pi$
$138$	3.33761	0.284116
$139$	13.3541	1.13268	0.566340	−	0.824172i	$-0.308359\pi$
$139$	13.3541	1.13268	0.566340	+	0.824172i	$0.308359\pi$
$140$	−0.199627	−0.0168715
$141$	−7.79272	−0.656266
$142$	−12.8438	−1.07783
$143$	1.32919	0.111152
$144$	0.608871	0.0507392
$145$	4.48825	0.372729
$146$	−9.16748	−0.758706
$147$	13.0240	1.07420
$148$	7.02354	0.577332
$149$	−19.0955	−1.56436	−0.782182	−	0.623050i	$-0.785893\pi$
$149$	−19.0955	−1.56436	−0.782182	+	0.623050i	$0.785893\pi$
$150$	8.97344	0.732678
$151$	−8.96904	−0.729890	−0.364945	−	0.931029i	$-0.618912\pi$
$151$	−8.96904	−0.729890	−0.364945	+	0.931029i	$0.618912\pi$
$152$	−1.00000	−0.0811107
$153$	0.645664	0.0521988
$154$	0.858836	0.0692070
$155$	0.743910	0.0597523
$156$	1.11638	0.0893818
$157$	−9.23601	−0.737114	−0.368557	−	0.929605i	$-0.620148\pi$
$157$	−9.23601	−0.737114	−0.368557	+	0.929605i	$0.620148\pi$
$158$	13.5143	1.07514
$159$	3.88214	0.307874
$160$	0.525736	0.0415631
$161$	0.667114	0.0525760
$162$	−10.4559	−0.821492
$163$	−16.1642	−1.26607	−0.633037	−	0.774121i	$-0.718192\pi$
$163$	−16.1642	−1.26607	−0.633037	+	0.774121i	$0.718192\pi$
$164$	1.12034	0.0874837
$165$	2.25899	0.175862
$166$	−9.65001	−0.748986
$167$	7.28272	0.563554	0.281777	−	0.959480i	$-0.409076\pi$
$167$	7.28272	0.563554	0.281777	+	0.959480i	$0.409076\pi$
$168$	0.721334	0.0556521
$169$	−12.6547	−0.973435
$170$	0.557505	0.0427587
$171$	−0.608871	−0.0465615
$172$	0.392283	0.0299113
$173$	−18.0036	−1.36879	−0.684393	−	0.729113i	$-0.739933\pi$
$173$	−18.0036	−1.36879	−0.684393	+	0.729113i	$0.739933\pi$
$174$	−16.2179	−1.22948
$175$	1.79359	0.135583
$176$	−2.26183	−0.170492
$177$	−17.5722	−1.32081
$178$	−17.4338	−1.30672
$179$	−12.0930	−0.903873	−0.451937	−	0.892050i	$-0.649267\pi$
$179$	−12.0930	−0.903873	−0.451937	+	0.892050i	$0.649267\pi$
$180$	0.320106	0.0238593
$181$	8.55501	0.635889	0.317945	−	0.948109i	$-0.397007\pi$
$181$	8.55501	0.635889	0.317945	+	0.948109i	$0.397007\pi$
$182$	0.223139	0.0165402
$183$	18.4555	1.36427
$184$	−1.75691	−0.129521
$185$	3.69253	0.271480
$186$	−2.68806	−0.197098
$187$	−2.39851	−0.175396
$188$	4.10208	0.299175
$189$	−1.72480	−0.125461
$190$	−0.525736	−0.0381409
$191$	−12.5757	−0.909944	−0.454972	−	0.890506i	$-0.650351\pi$
$191$	−12.5757	−0.909944	−0.454972	+	0.890506i	$0.650351\pi$
$192$	−1.89970	−0.137099
$193$	13.3939	0.964111	0.482056	−	0.876141i	$-0.339890\pi$
$193$	13.3939	0.964111	0.482056	+	0.876141i	$0.339890\pi$
$194$	6.85937	0.492474
$195$	0.586921	0.0420303
$196$	−6.85582	−0.489702
$197$	2.86371	0.204031	0.102016	−	0.994783i	$-0.467471\pi$
$197$	2.86371	0.204031	0.102016	+	0.994783i	$0.467471\pi$
$198$	−1.37716	−0.0978706
$199$	17.4605	1.23774	0.618871	−	0.785492i	$-0.287590\pi$
$199$	17.4605	1.23774	0.618871	+	0.785492i	$0.287590\pi$
$200$	−4.72360	−0.334009
$201$	−1.19166	−0.0840535
$202$	−4.67666	−0.329048
$203$	−3.24160	−0.227516
$204$	−2.01450	−0.141043
$205$	0.589002	0.0411377
$206$	−8.00413	−0.557674
$207$	−1.06973	−0.0743515
$208$	−0.587660	−0.0407469
$209$	2.26183	0.156454
$210$	0.379231	0.0261694
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−2.04355	−0.140352
$213$	24.3995	1.67182
$214$	8.49736	0.580867
$215$	0.206237	0.0140653
$216$	4.54243	0.309074
$217$	−0.537283	−0.0364731
$218$	−0.597719	−0.0404826
$219$	17.4155	1.17683
$220$	−1.18913	−0.0801708
$221$	−0.623170	−0.0419190
$222$	−13.3426	−0.895500
$223$	−0.371489	−0.0248768	−0.0124384	−	0.999923i	$-0.503959\pi$
$223$	−0.371489	−0.0248768	−0.0124384	+	0.999923i	$0.503959\pi$
$224$	−0.379709	−0.0253703
$225$	−2.87606	−0.191738
$226$	−6.43871	−0.428296
$227$	−26.0240	−1.72728	−0.863638	−	0.504112i	$-0.831820\pi$
$227$	−26.0240	−1.72728	−0.863638	+	0.504112i	$0.831820\pi$
$228$	1.89970	0.125811
$229$	7.62445	0.503838	0.251919	−	0.967748i	$-0.418938\pi$
$229$	7.62445	0.503838	0.251919	+	0.967748i	$0.418938\pi$
$230$	−0.923672	−0.0609051
$231$	−1.63153	−0.107347
$232$	8.53707	0.560486
$233$	27.2380	1.78442	0.892209	−	0.451623i	$-0.149155\pi$
$233$	27.2380	1.78442	0.892209	+	0.451623i	$0.149155\pi$
$234$	−0.357809	−0.0233907
$235$	2.15661	0.140682
$236$	9.24999	0.602123
$237$	−25.6732	−1.66765
$238$	−0.402654	−0.0261002
$239$	8.02940	0.519379	0.259689	−	0.965692i	$-0.416380\pi$
$239$	8.02940	0.519379	0.259689	+	0.965692i	$0.416380\pi$
$240$	−0.998743	−0.0644686
$241$	4.14056	0.266717	0.133359	−	0.991068i	$-0.457424\pi$
$241$	4.14056	0.266717	0.133359	+	0.991068i	$0.457424\pi$
$242$	−5.88413	−0.378246
$243$	6.23578	0.400025
$244$	−9.71496	−0.621937
$245$	−3.60435	−0.230274
$246$	−2.12831	−0.135696
$247$	0.587660	0.0373919
$248$	1.41499	0.0898518
$249$	18.3321	1.16175
$250$	−5.11205	−0.323314
$251$	14.7421	0.930515	0.465257	−	0.885175i	$-0.345962\pi$
$251$	14.7421	0.930515	0.465257	+	0.885175i	$0.345962\pi$
$252$	−0.231193	−0.0145638
$253$	3.97383	0.249833
$254$	13.2737	0.832865
$255$	−1.05909	−0.0663231
$256$	1.00000	0.0625000
$257$	8.10901	0.505826	0.252913	−	0.967489i	$-0.418611\pi$
$257$	8.10901	0.505826	0.252913	+	0.967489i	$0.418611\pi$
$258$	−0.745221	−0.0463955
$259$	−2.66690	−0.165713
$260$	−0.308954	−0.0191605
$261$	5.19797	0.321747
$262$	15.2992	0.945185
$263$	−24.7810	−1.52806	−0.764031	−	0.645179i	$-0.776783\pi$
$263$	−24.7810	−1.52806	−0.764031	+	0.645179i	$0.776783\pi$
$264$	4.29680	0.264450
$265$	−1.07437	−0.0659981
$266$	0.379709	0.0232814
$267$	33.1191	2.02685
$268$	0.627289	0.0383178
$269$	−10.7376	−0.654681	−0.327341	−	0.944906i	$-0.606152\pi$
$269$	−10.7376	−0.654681	−0.327341	+	0.944906i	$0.606152\pi$
$270$	2.38812	0.145337
$271$	−31.5092	−1.91405	−0.957024	−	0.290009i	$-0.906342\pi$
$271$	−31.5092	−1.91405	−0.957024	+	0.290009i	$0.906342\pi$
$272$	1.06043	0.0642979
$273$	−0.423899	−0.0256555
$274$	−17.7853	−1.07445
$275$	10.6840	0.644268
$276$	3.33761	0.200900
$277$	9.30654	0.559176	0.279588	−	0.960120i	$-0.409802\pi$
$277$	9.30654	0.559176	0.279588	+	0.960120i	$0.409802\pi$
$278$	13.3541	0.800925
$279$	0.861544	0.0515793
$280$	−0.199627	−0.0119300
$281$	−9.50032	−0.566742	−0.283371	−	0.959010i	$-0.591453\pi$
$281$	−9.50032	−0.566742	−0.283371	+	0.959010i	$0.591453\pi$
$282$	−7.79272	−0.464050
$283$	−12.9943	−0.772432	−0.386216	−	0.922408i	$-0.626218\pi$
$283$	−12.9943	−0.772432	−0.386216	+	0.922408i	$0.626218\pi$
$284$	−12.8438	−0.762142
$285$	0.998743	0.0591604
$286$	1.32919	0.0785964
$287$	−0.425402	−0.0251107
$288$	0.608871	0.0358781
$289$	−15.8755	−0.933853
$290$	4.48825	0.263559
$291$	−13.0308	−0.763877
$292$	−9.16748	−0.536486
$293$	−7.33455	−0.428489	−0.214244	−	0.976780i	$-0.568729\pi$
$293$	−7.33455	−0.428489	−0.214244	+	0.976780i	$0.568729\pi$
$294$	13.0240	0.759576
$295$	4.86306	0.283138
$296$	7.02354	0.408235
$297$	−10.2742	−0.596170
$298$	−19.0955	−1.10617
$299$	1.03247	0.0597090
$300$	8.97344	0.518082
$301$	−0.148953	−0.00858552
$302$	−8.96904	−0.516110
$303$	8.88426	0.510387
$304$	−1.00000	−0.0573539
$305$	−5.10751	−0.292455
$306$	0.645664	0.0369101
$307$	11.3366	0.647013	0.323507	−	0.946226i	$-0.395138\pi$
$307$	11.3366	0.647013	0.323507	+	0.946226i	$0.395138\pi$
$308$	0.858836	0.0489367
$309$	15.2055	0.865009
$310$	0.743910	0.0422513
$311$	−20.6640	−1.17175	−0.585873	−	0.810403i	$-0.699248\pi$
$311$	−20.6640	−1.17175	−0.585873	+	0.810403i	$0.699248\pi$
$312$	1.11638	0.0632025
$313$	−27.6984	−1.56560	−0.782802	−	0.622271i	$-0.786210\pi$
$313$	−27.6984	−1.56560	−0.782802	+	0.622271i	$0.786210\pi$
$314$	−9.23601	−0.521218
$315$	−0.121547	−0.00684839
$316$	13.5143	0.760239
$317$	−13.5183	−0.759265	−0.379632	−	0.925137i	$-0.623949\pi$
$317$	−13.5183	−0.759265	−0.379632	+	0.925137i	$0.623949\pi$
$318$	3.88214	0.217700
$319$	−19.3094	−1.08112
$320$	0.525736	0.0293896
$321$	−16.1425	−0.900984
$322$	0.667114	0.0371768
$323$	−1.06043	−0.0590038
$324$	−10.4559	−0.580883
$325$	2.77587	0.153978
$326$	−16.1642	−0.895250
$327$	1.13549	0.0627926
$328$	1.12034	0.0618603
$329$	−1.55759	−0.0858729
$330$	2.25899	0.124353
$331$	−5.21119	−0.286433	−0.143216	−	0.989691i	$-0.545744\pi$
$331$	−5.21119	−0.286433	−0.143216	+	0.989691i	$0.545744\pi$
$332$	−9.65001	−0.529613
$333$	4.27643	0.234347
$334$	7.28272	0.398493
$335$	0.329789	0.0180183
$336$	0.721334	0.0393520
$337$	−14.4348	−0.786315	−0.393158	−	0.919471i	$-0.628617\pi$
$337$	−14.4348	−0.786315	−0.393158	+	0.919471i	$0.628617\pi$
$338$	−12.6547	−0.688323
$339$	12.2316	0.664331
$340$	0.557505	0.0302350
$341$	−3.20046	−0.173315
$342$	−0.608871	−0.0329240
$343$	5.26117	0.284077
$344$	0.392283	0.0211505
$345$	1.75470	0.0944700
$346$	−18.0036	−0.967878
$347$	8.43130	0.452616	0.226308	−	0.974056i	$-0.427334\pi$
$347$	8.43130	0.452616	0.226308	+	0.974056i	$0.427334\pi$
$348$	−16.2179	−0.869371
$349$	0.00249019	0.000133297 0	6.66484e−5	−	1.00000i	$-0.499979\pi$
$349$	0.00249019	0.000133297 0	6.66484e−5		1.00000i	$0.499979\pi$
$350$	1.79359	0.0958715
$351$	−2.66941	−0.142482
$352$	−2.26183	−0.120556
$353$	22.4341	1.19405	0.597025	−	0.802223i	$-0.296349\pi$
$353$	22.4341	1.19405	0.597025	+	0.802223i	$0.296349\pi$
$354$	−17.5722	−0.933954
$355$	−6.75247	−0.358384
$356$	−17.4338	−0.923990
$357$	0.764922	0.0404840
$358$	−12.0930	−0.639135
$359$	17.4277	0.919797	0.459898	−	0.887972i	$-0.347886\pi$
$359$	17.4277	0.919797	0.459898	+	0.887972i	$0.347886\pi$
$360$	0.320106	0.0168710
$361$	1.00000	0.0526316
$362$	8.55501	0.449642
$363$	11.1781	0.586698
$364$	0.223139	0.0116957
$365$	−4.81968	−0.252273
$366$	18.4555	0.964686
$367$	22.1411	1.15576	0.577878	−	0.816123i	$-0.303881\pi$
$367$	22.1411	1.15576	0.577878	+	0.816123i	$0.303881\pi$
$368$	−1.75691	−0.0915853
$369$	0.682141	0.0355108
$370$	3.69253	0.191966
$371$	0.775955	0.0402856
$372$	−2.68806	−0.139369
$373$	−30.2812	−1.56790	−0.783951	−	0.620822i	$-0.786799\pi$
$373$	−30.2812	−1.56790	−0.783951	+	0.620822i	$0.786799\pi$
$374$	−2.39851	−0.124024
$375$	9.71138	0.501493
$376$	4.10208	0.211548
$377$	−5.01689	−0.258383
$378$	−1.72480	−0.0887142
$379$	−9.31729	−0.478597	−0.239298	−	0.970946i	$-0.576917\pi$
$379$	−9.31729	−0.478597	−0.239298	+	0.970946i	$0.576917\pi$
$380$	−0.525736	−0.0269697
$381$	−25.2160	−1.29186
$382$	−12.5757	−0.643428
$383$	−17.4149	−0.889857	−0.444929	−	0.895566i	$-0.646771\pi$
$383$	−17.4149	−0.889857	−0.444929	+	0.895566i	$0.646771\pi$
$384$	−1.89970	−0.0969438
$385$	0.451521	0.0230117
$386$	13.3939	0.681729
$387$	0.238850	0.0121414
$388$	6.85937	0.348232
$389$	15.3553	0.778547	0.389273	−	0.921122i	$-0.372726\pi$
$389$	15.3553	0.778547	0.389273	+	0.921122i	$0.372726\pi$
$390$	0.586921	0.0297199
$391$	−1.86308	−0.0942199
$392$	−6.85582	−0.346271
$393$	−29.0639	−1.46608
$394$	2.86371	0.144272
$395$	7.10496	0.357489
$396$	−1.37716	−0.0692050
$397$	−15.0797	−0.756827	−0.378414	−	0.925637i	$-0.623530\pi$
$397$	−15.0797	−0.756827	−0.378414	+	0.925637i	$0.623530\pi$
$398$	17.4605	0.875216
$399$	−0.721334	−0.0361118
$400$	−4.72360	−0.236180
$401$	−8.83791	−0.441344	−0.220672	−	0.975348i	$-0.570825\pi$
$401$	−8.83791	−0.441344	−0.220672	+	0.975348i	$0.570825\pi$
$402$	−1.19166	−0.0594348
$403$	−0.831531	−0.0414215
$404$	−4.67666	−0.232672
$405$	−5.49704	−0.273150
$406$	−3.24160	−0.160878
$407$	−15.8861	−0.787442
$408$	−2.01450	−0.0997325
$409$	−22.4127	−1.10824	−0.554119	−	0.832438i	$-0.686945\pi$
$409$	−22.4127	−1.10824	−0.554119	+	0.832438i	$0.686945\pi$
$410$	0.589002	0.0290888
$411$	33.7868	1.66658
$412$	−8.00413	−0.394335
$413$	−3.51230	−0.172829
$414$	−1.06973	−0.0525745
$415$	−5.07336	−0.249041
$416$	−0.587660	−0.0288124
$417$	−25.3688	−1.24232
$418$	2.26183	0.110630
$419$	−3.55275	−0.173563	−0.0867817	−	0.996227i	$-0.527658\pi$
$419$	−3.55275	−0.173563	−0.0867817	+	0.996227i	$0.527658\pi$
$420$	0.379231	0.0185046
$421$	12.1727	0.593261	0.296630	−	0.954992i	$-0.404137\pi$
$421$	12.1727	0.593261	0.296630	+	0.954992i	$0.404137\pi$
$422$	1.00000	0.0486792
$423$	2.49763	0.121439
$424$	−2.04355	−0.0992437
$425$	−5.00904	−0.242974
$426$	24.3995	1.18216
$427$	3.68885	0.178516
$428$	8.49736	0.410735
$429$	−2.52506	−0.121911
$430$	0.206237	0.00994566
$431$	−10.2473	−0.493594	−0.246797	−	0.969067i	$-0.579378\pi$
$431$	−10.2473	−0.493594	−0.246797	+	0.969067i	$0.579378\pi$
$432$	4.54243	0.218548
$433$	4.37829	0.210407	0.105204	−	0.994451i	$-0.466451\pi$
$433$	4.37829	0.210407	0.105204	+	0.994451i	$0.466451\pi$
$434$	−0.537283	−0.0257904
$435$	−8.52634	−0.408807
$436$	−0.597719	−0.0286255
$437$	1.75691	0.0840445
$438$	17.4155	0.832144
$439$	−17.0697	−0.814691	−0.407345	−	0.913274i	$-0.633546\pi$
$439$	−17.0697	−0.814691	−0.407345	+	0.913274i	$0.633546\pi$
$440$	−1.18913	−0.0566893
$441$	−4.17431	−0.198777
$442$	−0.623170	−0.0296412
$443$	0.413607	0.0196511	0.00982554	−	0.999952i	$-0.496872\pi$
$443$	0.413607	0.0196511	0.00982554	+	0.999952i	$0.496872\pi$
$444$	−13.3426	−0.633214
$445$	−9.16559	−0.434491
$446$	−0.371489	−0.0175905
$447$	36.2758	1.71579
$448$	−0.379709	−0.0179395
$449$	15.4057	0.727041	0.363521	−	0.931586i	$-0.381575\pi$
$449$	15.4057	0.727041	0.363521	+	0.931586i	$0.381575\pi$
$450$	−2.87606	−0.135579
$451$	−2.53401	−0.119322
$452$	−6.43871	−0.302851
$453$	17.0385	0.800539
$454$	−26.0240	−1.22137
$455$	0.117312	0.00549969
$456$	1.89970	0.0889617
$457$	9.71970	0.454668	0.227334	−	0.973817i	$-0.426999\pi$
$457$	9.71970	0.454668	0.227334	+	0.973817i	$0.426999\pi$
$458$	7.62445	0.356267
$459$	4.81692	0.224835
$460$	−0.923672	−0.0430664
$461$	−2.69422	−0.125482	−0.0627411	−	0.998030i	$-0.519984\pi$
$461$	−2.69422	−0.125482	−0.0627411	+	0.998030i	$0.519984\pi$
$462$	−1.63153	−0.0759058
$463$	7.24818	0.336851	0.168426	−	0.985714i	$-0.446132\pi$
$463$	7.24818	0.336851	0.168426	+	0.985714i	$0.446132\pi$
$464$	8.53707	0.396324
$465$	−1.41321	−0.0655360
$466$	27.2380	1.26177
$467$	15.6973	0.726386	0.363193	−	0.931714i	$-0.381687\pi$
$467$	15.6973	0.726386	0.363193	+	0.931714i	$0.381687\pi$
$468$	−0.357809	−0.0165397
$469$	−0.238187	−0.0109985
$470$	2.15661	0.0994770
$471$	17.5457	0.808462
$472$	9.24999	0.425765
$473$	−0.887277	−0.0407970
$474$	−25.6732	−1.17921
$475$	4.72360	0.216734
$476$	−0.402654	−0.0184556
$477$	−1.24426	−0.0569708
$478$	8.02940	0.367256
$479$	−4.74843	−0.216961	−0.108481	−	0.994099i	$-0.534599\pi$
$479$	−4.74843	−0.216961	−0.108481	+	0.994099i	$0.534599\pi$
$480$	−0.998743	−0.0455862
$481$	−4.12745	−0.188196
$482$	4.14056	0.188597
$483$	−1.26732	−0.0576650
$484$	−5.88413	−0.267461
$485$	3.60622	0.163750
$486$	6.23578	0.282861
$487$	−20.8859	−0.946432	−0.473216	−	0.880947i	$-0.656907\pi$
$487$	−20.8859	−0.946432	−0.473216	+	0.880947i	$0.656907\pi$
$488$	−9.71496	−0.439776
$489$	30.7071	1.38862
$490$	−3.60435	−0.162828
$491$	−6.67317	−0.301156	−0.150578	−	0.988598i	$-0.548113\pi$
$491$	−6.67317	−0.301156	−0.150578	+	0.988598i	$0.548113\pi$
$492$	−2.12831	−0.0959516
$493$	9.05295	0.407724
$494$	0.587660	0.0264401
$495$	−0.724024	−0.0325425
$496$	1.41499	0.0635348
$497$	4.87692	0.218760
$498$	18.3321	0.821483
$499$	−31.6783	−1.41811	−0.709057	−	0.705151i	$-0.750879\pi$
$499$	−31.6783	−1.41811	−0.709057	+	0.705151i	$0.750879\pi$
$500$	−5.11205	−0.228618
$501$	−13.8350	−0.618102
$502$	14.7421	0.657973
$503$	−33.8413	−1.50891	−0.754455	−	0.656352i	$-0.772099\pi$
$503$	−33.8413	−1.50891	−0.754455	+	0.656352i	$0.772099\pi$
$504$	−0.231193	−0.0102982
$505$	−2.45869	−0.109410
$506$	3.97383	0.176658
$507$	24.0401	1.06766
$508$	13.2737	0.588924
$509$	−6.23326	−0.276284	−0.138142	−	0.990412i	$-0.544113\pi$
$509$	−6.23326	−0.276284	−0.138142	+	0.990412i	$0.544113\pi$
$510$	−1.05909	−0.0468975
$511$	3.48097	0.153989
$512$	1.00000	0.0441942
$513$	−4.54243	−0.200553
$514$	8.10901	0.357673
$515$	−4.20806	−0.185429
$516$	−0.745221	−0.0328065
$517$	−9.27819	−0.408054
$518$	−2.66690	−0.117177
$519$	34.2014	1.50128
$520$	−0.308954	−0.0135485
$521$	25.2043	1.10422	0.552110	−	0.833771i	$-0.313823\pi$
$521$	25.2043	1.10422	0.552110	+	0.833771i	$0.313823\pi$
$522$	5.19797	0.227509
$523$	−18.5848	−0.812656	−0.406328	−	0.913727i	$-0.633191\pi$
$523$	−18.5848	−0.812656	−0.406328	+	0.913727i	$0.633191\pi$
$524$	15.2992	0.668347
$525$	−3.40729	−0.148706
$526$	−24.7810	−1.08050
$527$	1.50049	0.0653624
$528$	4.29680	0.186994
$529$	−19.9133	−0.865794
$530$	−1.07437	−0.0466677
$531$	5.63205	0.244410
$532$	0.379709	0.0164625
$533$	−0.658377	−0.0285175
$534$	33.1191	1.43320
$535$	4.46737	0.193141
$536$	0.627289	0.0270948
$537$	22.9731	0.991363
$538$	−10.7376	−0.462929
$539$	15.5067	0.667921
$540$	2.38812	0.102768
$541$	−7.43435	−0.319628	−0.159814	−	0.987147i	$-0.551089\pi$
$541$	−7.43435	−0.319628	−0.159814	+	0.987147i	$0.551089\pi$
$542$	−31.5092	−1.35344
$543$	−16.2520	−0.697439
$544$	1.06043	0.0454655
$545$	−0.314242	−0.0134607
$546$	−0.423899	−0.0181412
$547$	9.06417	0.387556	0.193778	−	0.981045i	$-0.437926\pi$
$547$	9.06417	0.387556	0.193778	+	0.981045i	$0.437926\pi$
$548$	−17.7853	−0.759751
$549$	−5.91516	−0.252453
$550$	10.6840	0.455566
$551$	−8.53707	−0.363691
$552$	3.33761	0.142058
$553$	−5.13150	−0.218213
$554$	9.30654	0.395397
$555$	−7.01471	−0.297758
$556$	13.3541	0.566340
$557$	−6.10311	−0.258597	−0.129299	−	0.991606i	$-0.541273\pi$
$557$	−6.10311	−0.258597	−0.129299	+	0.991606i	$0.541273\pi$
$558$	0.861544	0.0364721
$559$	−0.230529	−0.00975033
$560$	−0.199627	−0.00843576
$561$	4.55645	0.192373
$562$	−9.50032	−0.400747
$563$	−26.6611	−1.12363	−0.561815	−	0.827263i	$-0.689897\pi$
$563$	−26.6611	−1.12363	−0.561815	+	0.827263i	$0.689897\pi$
$564$	−7.79272	−0.328133
$565$	−3.38506	−0.142411
$566$	−12.9943	−0.546192
$567$	3.97019	0.166732
$568$	−12.8438	−0.538916
$569$	22.1617	0.929066	0.464533	−	0.885556i	$-0.346222\pi$
$569$	22.1617	0.929066	0.464533	+	0.885556i	$0.346222\pi$
$570$	0.998743	0.0418327
$571$	−9.99622	−0.418329	−0.209164	−	0.977880i	$-0.567074\pi$
$571$	−9.99622	−0.418329	−0.209164	+	0.977880i	$0.567074\pi$
$572$	1.32919	0.0555760
$573$	23.8900	0.998021
$574$	−0.425402	−0.0177559
$575$	8.29895	0.346090
$576$	0.608871	0.0253696
$577$	3.26324	0.135850	0.0679252	−	0.997690i	$-0.478362\pi$
$577$	3.26324	0.135850	0.0679252	+	0.997690i	$0.478362\pi$
$578$	−15.8755	−0.660333
$579$	−25.4444	−1.05743
$580$	4.48825	0.186364
$581$	3.66419	0.152016
$582$	−13.0308	−0.540143
$583$	4.62217	0.191431
$584$	−9.16748	−0.379353
$585$	−0.188113	−0.00777752
$586$	−7.33455	−0.302987
$587$	−5.89502	−0.243314	−0.121657	−	0.992572i	$-0.538821\pi$
$587$	−5.89502	−0.243314	−0.121657	+	0.992572i	$0.538821\pi$
$588$	13.0240	0.537102
$589$	−1.41499	−0.0583035
$590$	4.86306	0.200209
$591$	−5.44020	−0.223780
$592$	7.02354	0.288666
$593$	−22.6025	−0.928175	−0.464087	−	0.885789i	$-0.653618\pi$
$593$	−22.6025	−0.928175	−0.464087	+	0.885789i	$0.653618\pi$
$594$	−10.2742	−0.421556
$595$	−0.211690	−0.00867843
$596$	−19.0955	−0.782182
$597$	−33.1698	−1.35755
$598$	1.03247	0.0422207
$599$	−16.6886	−0.681877	−0.340938	−	0.940086i	$-0.610745\pi$
$599$	−16.6886	−0.681877	−0.340938	+	0.940086i	$0.610745\pi$
$600$	8.97344	0.366339
$601$	6.55961	0.267572	0.133786	−	0.991010i	$-0.457287\pi$
$601$	6.55961	0.267572	0.133786	+	0.991010i	$0.457287\pi$
$602$	−0.148953	−0.00607088
$603$	0.381938	0.0155537
$604$	−8.96904	−0.364945
$605$	−3.09350	−0.125769
$606$	8.88426	0.360898
$607$	18.4767	0.749947	0.374973	−	0.927036i	$-0.377652\pi$
$607$	18.4767	0.749947	0.374973	+	0.927036i	$0.377652\pi$
$608$	−1.00000	−0.0405554
$609$	6.15808	0.249538
$610$	−5.10751	−0.206797
$611$	−2.41062	−0.0975234
$612$	0.645664	0.0260994
$613$	−23.1283	−0.934142	−0.467071	−	0.884220i	$-0.654691\pi$
$613$	−23.1283	−0.934142	−0.467071	+	0.884220i	$0.654691\pi$
$614$	11.3366	0.457507
$615$	−1.11893	−0.0451196
$616$	0.858836	0.0346035
$617$	42.7339	1.72040	0.860201	−	0.509955i	$-0.170338\pi$
$617$	42.7339	1.72040	0.860201	+	0.509955i	$0.170338\pi$
$618$	15.2055	0.611653
$619$	14.2177	0.571456	0.285728	−	0.958311i	$-0.407765\pi$
$619$	14.2177	0.571456	0.285728	+	0.958311i	$0.407765\pi$
$620$	0.743910	0.0298762
$621$	−7.98065	−0.320253
$622$	−20.6640	−0.828550
$623$	6.61977	0.265216
$624$	1.11638	0.0446909
$625$	20.9304	0.837217
$626$	−27.6984	−1.10705
$627$	−4.29680	−0.171598
$628$	−9.23601	−0.368557
$629$	7.44796	0.296970
$630$	−0.121547	−0.00484254
$631$	38.5144	1.53324	0.766618	−	0.642104i	$-0.221938\pi$
$631$	38.5144	1.53324	0.766618	+	0.642104i	$0.221938\pi$
$632$	13.5143	0.537570
$633$	−1.89970	−0.0755064
$634$	−13.5183	−0.536881
$635$	6.97846	0.276932
$636$	3.88214	0.153937
$637$	4.02889	0.159630
$638$	−19.3094	−0.764466
$639$	−7.82024	−0.309364
$640$	0.525736	0.0207816
$641$	30.0296	1.18610	0.593049	−	0.805166i	$-0.297924\pi$
$641$	30.0296	1.18610	0.593049	+	0.805166i	$0.297924\pi$
$642$	−16.1425	−0.637092
$643$	35.0197	1.38104	0.690521	−	0.723312i	$-0.257381\pi$
$643$	35.0197	1.38104	0.690521	+	0.723312i	$0.257381\pi$
$644$	0.667114	0.0262880
$645$	−0.391790	−0.0154267
$646$	−1.06043	−0.0417220
$647$	12.1410	0.477312	0.238656	−	0.971104i	$-0.423293\pi$
$647$	12.1410	0.477312	0.238656	+	0.971104i	$0.423293\pi$
$648$	−10.4559	−0.410746
$649$	−20.9219	−0.821256
$650$	2.77587	0.108879
$651$	1.02068	0.0400035
$652$	−16.1642	−0.633037
$653$	3.14628	0.123124	0.0615618	−	0.998103i	$-0.480392\pi$
$653$	3.14628	0.123124	0.0615618	+	0.998103i	$0.480392\pi$
$654$	1.13549	0.0444011
$655$	8.04332	0.314279
$656$	1.12034	0.0437418
$657$	−5.58181	−0.217767
$658$	−1.55759	−0.0607213
$659$	−46.4904	−1.81101	−0.905504	−	0.424338i	$-0.860507\pi$
$659$	−46.4904	−1.81101	−0.905504	+	0.424338i	$0.860507\pi$
$660$	2.25899	0.0879309
$661$	−12.5184	−0.486910	−0.243455	−	0.969912i	$-0.578281\pi$
$661$	−12.5184	−0.486910	−0.243455	+	0.969912i	$0.578281\pi$
$662$	−5.21119	−0.202539
$663$	1.18384	0.0459765
$664$	−9.65001	−0.374493
$665$	0.199627	0.00774119
$666$	4.27643	0.165708
$667$	−14.9989	−0.580759
$668$	7.28272	0.281777
$669$	0.705719	0.0272847
$670$	0.329789	0.0127409
$671$	21.9736	0.848280
$672$	0.721334	0.0278260
$673$	−33.5915	−1.29486	−0.647428	−	0.762127i	$-0.724155\pi$
$673$	−33.5915	−1.29486	−0.647428	+	0.762127i	$0.724155\pi$
$674$	−14.4348	−0.556009
$675$	−21.4567	−0.825867
$676$	−12.6547	−0.486718
$677$	−0.594571	−0.0228512	−0.0114256	−	0.999935i	$-0.503637\pi$
$677$	−0.594571	−0.0228512	−0.0114256	+	0.999935i	$0.503637\pi$
$678$	12.2316	0.469753
$679$	−2.60456	−0.0999540
$680$	0.557505	0.0213794
$681$	49.4379	1.89447
$682$	−3.20046	−0.122552
$683$	34.8040	1.33174	0.665869	−	0.746068i	$-0.268061\pi$
$683$	34.8040	1.33174	0.665869	+	0.746068i	$0.268061\pi$
$684$	−0.608871	−0.0232808
$685$	−9.35038	−0.357260
$686$	5.26117	0.200873
$687$	−14.4842	−0.552606
$688$	0.392283	0.0149557
$689$	1.20091	0.0457512
$690$	1.75470	0.0668004
$691$	−7.75069	−0.294850	−0.147425	−	0.989073i	$-0.547099\pi$
$691$	−7.75069	−0.294850	−0.147425	+	0.989073i	$0.547099\pi$
$692$	−18.0036	−0.684393
$693$	0.522920	0.0198641
$694$	8.43130	0.320048
$695$	7.02073	0.266311
$696$	−16.2179	−0.614738
$697$	1.18804	0.0450001
$698$	0.00249019	9.42551e−5 0
$699$	−51.7440	−1.95714
$700$	1.79359	0.0677914
$701$	−16.2042	−0.612023	−0.306012	−	0.952028i	$-0.598995\pi$
$701$	−16.2042	−0.612023	−0.306012	+	0.952028i	$0.598995\pi$
$702$	−2.66941	−0.100750
$703$	−7.02354	−0.264898
$704$	−2.26183	−0.0852459
$705$	−4.09692	−0.154299
$706$	22.4341	0.844320
$707$	1.77577	0.0667846
$708$	−17.5722	−0.660405
$709$	−6.06348	−0.227719	−0.113859	−	0.993497i	$-0.536321\pi$
$709$	−6.06348	−0.227719	−0.113859	+	0.993497i	$0.536321\pi$
$710$	−6.75247	−0.253416
$711$	8.22847	0.308592
$712$	−17.4338	−0.653360
$713$	−2.48601	−0.0931017
$714$	0.764922	0.0286265
$715$	0.698801	0.0261337
$716$	−12.0930	−0.451937
$717$	−15.2535	−0.569651
$718$	17.4277	0.650395
$719$	−20.7821	−0.775043	−0.387521	−	0.921861i	$-0.626669\pi$
$719$	−20.7821	−0.775043	−0.387521	+	0.921861i	$0.626669\pi$
$720$	0.320106	0.0119296
$721$	3.03924	0.113187
$722$	1.00000	0.0372161
$723$	−7.86584	−0.292534
$724$	8.55501	0.317945
$725$	−40.3257	−1.49766
$726$	11.1781	0.414858
$727$	37.9812	1.40864	0.704322	−	0.709881i	$-0.251251\pi$
$727$	37.9812	1.40864	0.704322	+	0.709881i	$0.251251\pi$
$728$	0.223139	0.00827010
$729$	19.5215	0.723020
$730$	−4.81968	−0.178384
$731$	0.415988	0.0153859
$732$	18.4555	0.682136
$733$	−19.4216	−0.717352	−0.358676	−	0.933462i	$-0.616772\pi$
$733$	−19.4216	−0.717352	−0.358676	+	0.933462i	$0.616772\pi$
$734$	22.1411	0.817243
$735$	6.84720	0.252563
$736$	−1.75691	−0.0647606
$737$	−1.41882	−0.0522630
$738$	0.682141	0.0251100
$739$	12.3527	0.454402	0.227201	−	0.973848i	$-0.427043\pi$
$739$	12.3527	0.454402	0.227201	+	0.973848i	$0.427043\pi$
$740$	3.69253	0.135740
$741$	−1.11638	−0.0410112
$742$	0.775955	0.0284862
$743$	−8.88293	−0.325883	−0.162942	−	0.986636i	$-0.552098\pi$
$743$	−8.88293	−0.325883	−0.162942	+	0.986636i	$0.552098\pi$
$744$	−2.68806	−0.0985489
$745$	−10.0392	−0.367808
$746$	−30.2812	−1.10867
$747$	−5.87561	−0.214977
$748$	−2.39851	−0.0876981
$749$	−3.22652	−0.117894
$750$	9.71138	0.354609
$751$	6.59694	0.240726	0.120363	−	0.992730i	$-0.461594\pi$
$751$	6.59694	0.240726	0.120363	+	0.992730i	$0.461594\pi$
$752$	4.10208	0.149587
$753$	−28.0057	−1.02058
$754$	−5.01689	−0.182704
$755$	−4.71535	−0.171609
$756$	−1.72480	−0.0627304
$757$	−44.2589	−1.60862	−0.804308	−	0.594213i	$-0.797464\pi$
$757$	−44.2589	−1.60862	−0.804308	+	0.594213i	$0.797464\pi$
$758$	−9.31729	−0.338419
$759$	−7.54910	−0.274015
$760$	−0.525736	−0.0190705
$761$	45.6870	1.65615	0.828077	−	0.560615i	$-0.189435\pi$
$761$	45.6870	1.65615	0.828077	+	0.560615i	$0.189435\pi$
$762$	−25.2160	−0.913481
$763$	0.226959	0.00821646
$764$	−12.5757	−0.454972
$765$	0.339449	0.0122728
$766$	−17.4149	−0.629224
$767$	−5.43585	−0.196277
$768$	−1.89970	−0.0685496
$769$	19.4790	0.702430	0.351215	−	0.936295i	$-0.385769\pi$
$769$	19.4790	0.702430	0.351215	+	0.936295i	$0.385769\pi$
$770$	0.451521	0.0162717
$771$	−15.4047	−0.554787
$772$	13.3939	0.482056
$773$	50.2393	1.80698	0.903490	−	0.428608i	$-0.140996\pi$
$773$	50.2393	1.80698	0.903490	+	0.428608i	$0.140996\pi$
$774$	0.238850	0.00858528
$775$	−6.68383	−0.240090
$776$	6.85937	0.246237
$777$	5.06632	0.181753
$778$	15.3553	0.550516
$779$	−1.12034	−0.0401403
$780$	0.586921	0.0210151
$781$	29.0506	1.03951
$782$	−1.86308	−0.0666235
$783$	38.7791	1.38585
$784$	−6.85582	−0.244851
$785$	−4.85570	−0.173308
$786$	−29.0639	−1.03667
$787$	−0.890521	−0.0317436	−0.0158718	−	0.999874i	$-0.505052\pi$
$787$	−0.890521	−0.0317436	−0.0158718	+	0.999874i	$0.505052\pi$
$788$	2.86371	0.102016
$789$	47.0765	1.67597
$790$	7.10496	0.252783
$791$	2.44483	0.0869283
$792$	−1.37716	−0.0489353
$793$	5.70909	0.202736
$794$	−15.0797	−0.535158
$795$	2.04098	0.0723863
$796$	17.4605	0.618871
$797$	−9.32153	−0.330186	−0.165093	−	0.986278i	$-0.552792\pi$
$797$	−9.32153	−0.330186	−0.165093	+	0.986278i	$0.552792\pi$
$798$	−0.721334	−0.0255349
$799$	4.34995	0.153890
$800$	−4.72360	−0.167005
$801$	−10.6149	−0.375061
$802$	−8.83791	−0.312077
$803$	20.7353	0.731732
$804$	−1.19166	−0.0420267
$805$	0.350726	0.0123615
$806$	−0.831531	−0.0292894
$807$	20.3982	0.718050
$808$	−4.67666	−0.164524
$809$	−37.9284	−1.33349	−0.666746	−	0.745285i	$-0.732313\pi$
$809$	−37.9284	−1.33349	−0.666746	+	0.745285i	$0.732313\pi$
$810$	−5.49704	−0.193146
$811$	16.4663	0.578209	0.289105	−	0.957297i	$-0.406642\pi$
$811$	16.4663	0.578209	0.289105	+	0.957297i	$0.406642\pi$
$812$	−3.24160	−0.113758
$813$	59.8581	2.09932
$814$	−15.8861	−0.556806
$815$	−8.49808	−0.297675
$816$	−2.01450	−0.0705215
$817$	−0.392283	−0.0137242
$818$	−22.4127	−0.783642
$819$	0.135863	0.00474744
$820$	0.589002	0.0205689
$821$	−39.7439	−1.38707	−0.693536	−	0.720422i	$-0.743948\pi$
$821$	−39.7439	−1.38707	−0.693536	+	0.720422i	$0.743948\pi$
$822$	33.7868	1.17845
$823$	8.91256	0.310672	0.155336	−	0.987862i	$-0.450354\pi$
$823$	8.91256	0.310672	0.155336	+	0.987862i	$0.450354\pi$
$824$	−8.00413	−0.278837
$825$	−20.2964	−0.706629
$826$	−3.51230	−0.122209
$827$	28.8153	1.00201	0.501004	−	0.865445i	$-0.332964\pi$
$827$	28.8153	1.00201	0.501004	+	0.865445i	$0.332964\pi$
$828$	−1.06973	−0.0371758
$829$	−9.08668	−0.315594	−0.157797	−	0.987472i	$-0.550439\pi$
$829$	−9.08668	−0.315594	−0.157797	+	0.987472i	$0.550439\pi$
$830$	−5.07336	−0.176099
$831$	−17.6797	−0.613301
$832$	−0.587660	−0.0203734
$833$	−7.27010	−0.251894
$834$	−25.3688	−0.878450
$835$	3.82879	0.132501
$836$	2.26183	0.0782270
$837$	6.42749	0.222166
$838$	−3.55275	−0.122728
$839$	55.6230	1.92032	0.960159	−	0.279455i	$-0.0901536\pi$
$839$	55.6230	1.92032	0.960159	+	0.279455i	$0.0901536\pi$
$840$	0.379231	0.0130847
$841$	43.8816	1.51316
$842$	12.1727	0.419499
$843$	18.0478	0.621599
$844$	1.00000	0.0344214
$845$	−6.65301	−0.228871
$846$	2.49763	0.0858704
$847$	2.23426	0.0767699
$848$	−2.04355	−0.0701759
$849$	24.6853	0.847199
$850$	−5.00904	−0.171809
$851$	−12.3397	−0.423001
$852$	24.3995	0.835912
$853$	−13.2423	−0.453407	−0.226703	−	0.973964i	$-0.572795\pi$
$853$	−13.2423	−0.453407	−0.226703	+	0.973964i	$0.572795\pi$
$854$	3.68885	0.126230
$855$	−0.320106	−0.0109474
$856$	8.49736	0.290434
$857$	−5.47667	−0.187079	−0.0935397	−	0.995616i	$-0.529818\pi$
$857$	−5.47667	−0.187079	−0.0935397	+	0.995616i	$0.529818\pi$
$858$	−2.52506	−0.0862040
$859$	4.94508	0.168724	0.0843619	−	0.996435i	$-0.473115\pi$
$859$	4.94508	0.168724	0.0843619	+	0.996435i	$0.473115\pi$
$860$	0.206237	0.00703264
$861$	0.808137	0.0275412
$862$	−10.2473	−0.349024
$863$	15.9190	0.541889	0.270944	−	0.962595i	$-0.412664\pi$
$863$	15.9190	0.541889	0.270944	+	0.962595i	$0.412664\pi$
$864$	4.54243	0.154537
$865$	−9.46513	−0.321824
$866$	4.37829	0.148780
$867$	30.1587	1.02424
$868$	−0.537283	−0.0182366
$869$	−30.5670	−1.03692
$870$	−8.52634	−0.289070
$871$	−0.368633	−0.0124906
$872$	−0.597719	−0.0202413
$873$	4.17647	0.141352
$874$	1.75691	0.0594284
$875$	1.94109	0.0656208
$876$	17.4155	0.588415
$877$	−57.6654	−1.94722	−0.973611	−	0.228216i	$-0.926711\pi$
$877$	−57.6654	−1.94722	−0.973611	+	0.228216i	$0.926711\pi$
$878$	−17.0697	−0.576074
$879$	13.9335	0.469964
$880$	−1.18913	−0.0400854
$881$	−19.8040	−0.667215	−0.333608	−	0.942712i	$-0.608266\pi$
$881$	−19.8040	−0.667215	−0.333608	+	0.942712i	$0.608266\pi$
$882$	−4.17431	−0.140556
$883$	−10.8911	−0.366516	−0.183258	−	0.983065i	$-0.558664\pi$
$883$	−10.8911	−0.366516	−0.183258	+	0.983065i	$0.558664\pi$
$884$	−0.623170	−0.0209595
$885$	−9.23836	−0.310544
$886$	0.413607	0.0138954
$887$	12.8293	0.430767	0.215384	−	0.976530i	$-0.430900\pi$
$887$	12.8293	0.430767	0.215384	+	0.976530i	$0.430900\pi$
$888$	−13.3426	−0.447750
$889$	−5.04013	−0.169041
$890$	−9.16559	−0.307231
$891$	23.6494	0.792286
$892$	−0.371489	−0.0124384
$893$	−4.10208	−0.137271
$894$	36.2758	1.21324
$895$	−6.35773	−0.212515
$896$	−0.379709	−0.0126852
$897$	−1.96138	−0.0654885
$898$	15.4057	0.514096
$899$	12.0798	0.402885
$900$	−2.87606	−0.0958688
$901$	−2.16704	−0.0721946
$902$	−2.53401	−0.0843734
$903$	0.282967	0.00941655
$904$	−6.43871	−0.214148
$905$	4.49768	0.149508
$906$	17.0385	0.566066
$907$	30.5152	1.01324	0.506620	−	0.862170i	$-0.330895\pi$
$907$	30.5152	1.01324	0.506620	+	0.862170i	$0.330895\pi$
$908$	−26.0240	−0.863638
$909$	−2.84748	−0.0944450
$910$	0.117312	0.00388887
$911$	20.5620	0.681249	0.340625	−	0.940199i	$-0.389361\pi$
$911$	20.5620	0.681249	0.340625	+	0.940199i	$0.389361\pi$
$912$	1.89970	0.0629054
$913$	21.8267	0.722357
$914$	9.71970	0.321499
$915$	9.70275	0.320763
$916$	7.62445	0.251919
$917$	−5.80922	−0.191837
$918$	4.81692	0.158982
$919$	21.9428	0.723828	0.361914	−	0.932212i	$-0.382123\pi$
$919$	21.9428	0.723828	0.361914	+	0.932212i	$0.382123\pi$
$920$	−0.923672	−0.0304526
$921$	−21.5361	−0.709640
$922$	−2.69422	−0.0887293
$923$	7.54781	0.248439
$924$	−1.63153	−0.0536735
$925$	−33.1764	−1.09083
$926$	7.24818	0.238190
$927$	−4.87348	−0.160066
$928$	8.53707	0.280243
$929$	32.7431	1.07426	0.537132	−	0.843498i	$-0.319508\pi$
$929$	32.7431	1.07426	0.537132	+	0.843498i	$0.319508\pi$
$930$	−1.41321	−0.0463409
$931$	6.85582	0.224690
$932$	27.2380	0.892209
$933$	39.2554	1.28516
$934$	15.6973	0.513633
$935$	−1.26098	−0.0412385
$936$	−0.357809	−0.0116953
$937$	−50.1812	−1.63935	−0.819674	−	0.572830i	$-0.805846\pi$
$937$	−50.1812	−1.63935	−0.819674	+	0.572830i	$0.805846\pi$
$938$	−0.238187	−0.00777709
$939$	52.6187	1.71715
$940$	2.15661	0.0703409
$941$	55.6880	1.81538	0.907689	−	0.419644i	$-0.137845\pi$
$941$	55.6880	1.81538	0.907689	+	0.419644i	$0.137845\pi$
$942$	17.5457	0.571669
$943$	−1.96833	−0.0640978
$944$	9.24999	0.301062
$945$	−0.906791	−0.0294979
$946$	−0.887277	−0.0288479
$947$	−10.5067	−0.341422	−0.170711	−	0.985321i	$-0.554606\pi$
$947$	−10.5067	−0.341422	−0.170711	+	0.985321i	$0.554606\pi$
$948$	−25.6732	−0.833826
$949$	5.38736	0.174881
$950$	4.72360	0.153254
$951$	25.6808	0.832757
$952$	−0.402654	−0.0130501
$953$	−23.1307	−0.749277	−0.374638	−	0.927171i	$-0.622233\pi$
$953$	−23.1307	−0.749277	−0.374638	+	0.927171i	$0.622233\pi$
$954$	−1.24426	−0.0402844
$955$	−6.61149	−0.213943
$956$	8.02940	0.259689
$957$	36.6821	1.18576
$958$	−4.74843	−0.153415
$959$	6.75324	0.218073
$960$	−0.998743	−0.0322343
$961$	−28.9978	−0.935413
$962$	−4.12745	−0.133074
$963$	5.17379	0.166723
$964$	4.14056	0.133359
$965$	7.04164	0.226678
$966$	−1.26732	−0.0407753
$967$	−52.4284	−1.68598	−0.842992	−	0.537926i	$-0.819208\pi$
$967$	−52.4284	−1.68598	−0.842992	+	0.537926i	$0.819208\pi$
$968$	−5.88413	−0.189123
$969$	2.01450	0.0647150
$970$	3.60622	0.115789
$971$	−5.51109	−0.176859	−0.0884296	−	0.996082i	$-0.528185\pi$
$971$	−5.51109	−0.176859	−0.0884296	+	0.996082i	$0.528185\pi$
$972$	6.23578	0.200013
$973$	−5.07066	−0.162558
$974$	−20.8859	−0.669228
$975$	−5.27333	−0.168882
$976$	−9.71496	−0.310968
$977$	42.8121	1.36968	0.684840	−	0.728693i	$-0.259872\pi$
$977$	42.8121	1.36968	0.684840	+	0.728693i	$0.259872\pi$
$978$	30.7071	0.981904
$979$	39.4323	1.26026
$980$	−3.60435	−0.115137
$981$	−0.363933	−0.0116195
$982$	−6.67317	−0.212949
$983$	−0.940855	−0.0300086	−0.0150043	−	0.999887i	$-0.504776\pi$
$983$	−0.940855	−0.0300086	−0.0150043	+	0.999887i	$0.504776\pi$
$984$	−2.12831	−0.0678480
$985$	1.50556	0.0479710
$986$	9.05295	0.288305
$987$	2.95896	0.0941849
$988$	0.587660	0.0186959
$989$	−0.689207	−0.0219155
$990$	−0.724024	−0.0230110
$991$	−0.610827	−0.0194036	−0.00970178	−	0.999953i	$-0.503088\pi$
$991$	−0.610827	−0.0194036	−0.00970178	+	0.999953i	$0.503088\pi$
$992$	1.41499	0.0449259
$993$	9.89971	0.314158
$994$	4.87692	0.154686
$995$	9.17963	0.291014
$996$	18.3321	0.580876
$997$	−2.28042	−0.0722215	−0.0361108	−	0.999348i	$-0.511497\pi$
$997$	−2.28042	−0.0722215	−0.0361108	+	0.999348i	$0.511497\pi$
$998$	−31.6783	−1.00276
$999$	31.9040	1.00940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.9	✓	32	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.89970 q^{3} +1.00000 q^{4} +0.525736 q^{5} -1.89970 q^{6} -0.379709 q^{7} +1.00000 q^{8} +0.608871 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.89970 q^{3} +1.00000 q^{4} +0.525736 q^{5} -1.89970 q^{6} -0.379709 q^{7} +1.00000 q^{8} +0.608871 q^{9} +0.525736 q^{10} -2.26183 q^{11} -1.89970 q^{12} -0.587660 q^{13} -0.379709 q^{14} -0.998743 q^{15} +1.00000 q^{16} +1.06043 q^{17} +0.608871 q^{18} -1.00000 q^{19} +0.525736 q^{20} +0.721334 q^{21} -2.26183 q^{22} -1.75691 q^{23} -1.89970 q^{24} -4.72360 q^{25} -0.587660 q^{26} +4.54243 q^{27} -0.379709 q^{28} +8.53707 q^{29} -0.998743 q^{30} +1.41499 q^{31} +1.00000 q^{32} +4.29680 q^{33} +1.06043 q^{34} -0.199627 q^{35} +0.608871 q^{36} +7.02354 q^{37} -1.00000 q^{38} +1.11638 q^{39} +0.525736 q^{40} +1.12034 q^{41} +0.721334 q^{42} +0.392283 q^{43} -2.26183 q^{44} +0.320106 q^{45} -1.75691 q^{46} +4.10208 q^{47} -1.89970 q^{48} -6.85582 q^{49} -4.72360 q^{50} -2.01450 q^{51} -0.587660 q^{52} -2.04355 q^{53} +4.54243 q^{54} -1.18913 q^{55} -0.379709 q^{56} +1.89970 q^{57} +8.53707 q^{58} +9.24999 q^{59} -0.998743 q^{60} -9.71496 q^{61} +1.41499 q^{62} -0.231193 q^{63} +1.00000 q^{64} -0.308954 q^{65} +4.29680 q^{66} +0.627289 q^{67} +1.06043 q^{68} +3.33761 q^{69} -0.199627 q^{70} -12.8438 q^{71} +0.608871 q^{72} -9.16748 q^{73} +7.02354 q^{74} +8.97344 q^{75} -1.00000 q^{76} +0.858836 q^{77} +1.11638 q^{78} +13.5143 q^{79} +0.525736 q^{80} -10.4559 q^{81} +1.12034 q^{82} -9.65001 q^{83} +0.721334 q^{84} +0.557505 q^{85} +0.392283 q^{86} -16.2179 q^{87} -2.26183 q^{88} -17.4338 q^{89} +0.320106 q^{90} +0.223139 q^{91} -1.75691 q^{92} -2.68806 q^{93} +4.10208 q^{94} -0.525736 q^{95} -1.89970 q^{96} +6.85937 q^{97} -6.85582 q^{98} -1.37716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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